Object identification system and method

ABSTRACT

A method of tracking an object including producing a guided surface wave with a guided surface waveguide probe, the guided surface wave having sufficient energy density to power object identification tags across an area of interest; receiving return signals from a tag of interest at plural receivers, the tag of interest associated with an object and the receivers that receive the return signals change over time as the tag moves with the associated object in the area of interest; and identifying a series of geolocations at which the object was present as a function of time according to the received reply signals from the tag.

RELATED APPLICATION DATA

This application is related to co-pending U.S. Non-provisional patentapplication entitled “Excitation and Use of Guided Surface Wave Modes onLossy Media,” which was filed on Mar. 7, 2013 and assigned applicationSer. No. 13/789,538, and was published on Sep. 11, 2014 as PublicationNumber US2014/0252886 A1, and which is incorporated herein by referencein its entirety. This application is also related to co-pending U.S.Non-provisional patent application entitled “Excitation and Use ofGuided Surface Wave Modes on Lossy Media,” which was filed on Mar. 7,2013 and assigned application Ser. No. 13/789,525, and was published onSep. 11, 2014 as Publication Number US2014/0252865 A1, and which isincorporated herein by reference in its entirety. This application isfurther related to co-pending U.S. Non-provisional patent applicationentitled “Excitation and Use of Guided Surface Wave Modes on LossyMedia,” which was filed on Sep. 10, 2014 and assigned application Ser.No. 14/483,089, and which is incorporated herein by reference in itsentirety. This application is further related to co-pending U.S.Non-provisional patent application entitled “Excitation and Use ofGuided Surface Waves,” which was filed on Jun. 2, 2015 and assignedapplication Ser. No. 14/728,507, and which is incorporated herein byreference in its entirety. This application is further related toco-pending U.S. Non-provisional patent application entitled “Excitationand Use of Guided Surface Waves,” which was filed on Jun. 2, 2015 andassigned application Ser. No. 14/728,492, and which is incorporatedherein by reference in its entirety.

BACKGROUND

For over a century, radio wave signals have been transmitted usingconventional antenna structures. In contrast to radio science,electrical power distribution has relied on guiding electrical energyalong electrical conductors such as wires. This understanding of thedistinction between radio frequency (RF) and power transmission hasexisted since the early 1900's.

Radio frequency identification (RFID) systems, however, have used RFenergy that is emitted from a reader device to power tags. The tags mayaffect the emitted signal to invoke a change in the emitted signal thatis detectable by the reader device or the tags may transmit an RF signalthat is detectable by the reader device. In the former case, the readermay be able to determine that a tag is within an operable range of thereader device. In the later case, the reader may be able to extract acode that uniquely identifies the tag from the signal output by the tag.The range of RFID systems is severely limited. Also, the capabilities ofthe tags are limited due to the small amount of useable energy that maybe derived from the RF signal emitted by the reader device.

BRIEF DESCRIPTION OF THE DRAWINGS

Aspects of the present disclosure are better understood with referenceto the following drawings. The drawings are not necessarily to scale,emphasis instead being placed upon clearly illustrating the principlesof the disclosure. Moreover, in the drawings, like reference numeralsdesignate corresponding parts throughout the several views.

FIG. 1 is a chart that depicts field strength as a function of distancefor a guided electromagnetic field and a radiated electromagnetic field.

FIG. 2 is a drawing that illustrates a propagation interface with tworegions employed for transmission of a guided surface wave according tovarious embodiments of the present disclosure.

FIG. 3 is a drawing that illustrates a guided surface waveguide probedisposed with respect to a propagation interface of FIG. 2 according tovarious embodiments of the present disclosure.

FIG. 4 is a plot of an example of the magnitudes of close-in and far-outasymptotes of first order Hankel functions according to variousembodiments of the present disclosure.

FIGS. 5A and 5B are drawings that illustrate a complex angle ofincidence of an electric field synthesized by a guided surface waveguideprobe according to various embodiments of the present disclosure.

FIG. 6 is a graphical representation illustrating the effect ofelevation of a charge terminal on the location where the electric fieldof FIG. 5A intersects with the lossy conducting medium at a Brewsterangle according to various embodiments of the present disclosure.

FIG. 7 is a graphical representation of an example of a guided surfacewaveguide probe according to various embodiments of the presentdisclosure.

FIGS. 8A through 8C are graphical representations illustrating examplesof equivalent image plane models of the guided surface waveguide probeof FIGS. 3 and 7 according to various embodiments of the presentdisclosure.

FIGS. 9A and 9B are graphical representations illustrating examples ofsingle-wire transmission line and classic transmission line models ofthe equivalent image plane models of FIGS. 8B and 8C according tovarious embodiments of the present disclosure.

FIG. 10 is a flow chart illustrating an example of adjusting a guidedsurface waveguide probe of FIGS. 3 and 7 to launch a guided surface wavealong the surface of a lossy conducting medium according to variousembodiments of the present disclosure.

FIG. 11 is a plot illustrating an example of the relationship between awave tilt angle and the phase delay of a guided surface waveguide probeof FIGS. 3 and 7 according to various embodiments of the presentdisclosure.

FIG. 12 is a drawing that illustrates an example of a guided surfacewaveguide probe according to various embodiments of the presentdisclosure.

FIG. 13 is a graphical representation illustrating the incidence of asynthesized electric field at a complex Brewster angle to match theguided surface waveguide mode at the Hankel crossover distance accordingto various embodiments of the present disclosure.

FIG. 14 is a graphical representation of an example of a guided surfacewaveguide probe of FIG. 12 according to various embodiments of thepresent disclosure.

FIG. 15A includes plots of an example of the imaginary and real parts ofa phase delay (Φ_(U)) of a charge terminal T₁ of a guided surfacewaveguide probe according to various embodiments of the presentdisclosure.

FIG. 15B is a schematic diagram of the guided surface waveguide probe ofFIG. 14 according to various embodiments of the present disclosure.

FIG. 16 is a drawing that illustrates an example of a guided surfacewaveguide probe according to various embodiments of the presentdisclosure.

FIG. 17 is a graphical representation of an example of a guided surfacewaveguide probe of FIG. 16 according to various embodiments of thepresent disclosure.

FIGS. 18A through 18C depict examples of receiving structures that canbe employed to receive energy transmitted in the form of a guidedsurface wave launched by a guided surface waveguide probe according tothe various embodiments of the present disclosure.

FIG. 18D is a flow chart illustrating an example of adjusting areceiving structure according to various embodiments of the presentdisclosure.

FIG. 19 depicts an example of an additional receiving structure that canbe employed to receive energy transmitted in the form of a guidedsurface wave launched by a guided surface waveguide probe according tothe various embodiments of the present disclosure.

FIG. 20A shows a symbol that generically represents a guided surfacewave waveguide probe.

FIG. 20B shows a symbol that generically represents a guided surfacewave receive structure.

FIG. 20C shows a symbol that generically represents a linear probe typeof guided surface wave receive structure.

FIG. 20D shows a symbol that generically represents a tuned resonatortype of guided surface wave receive structure.

FIG. 20E shows a symbol that generically represents a magnetic coil typeof guided surface wave receive structure.

FIG. 21 is a schematic illustration of one embodiment of an objectidentification system.

FIG. 22 is a schematic illustration of another embodiment of an objectidentification system.

FIG. 23 is a schematic illustration of a tag that is used as part of theobject identification system.

FIG. 24 is a schematic view of first and second object identificationsystems deployed at neighboring sites.

FIG. 25 is a schematic view of an object identification system deployedto identify objects over a wide area.

FIG. 26 is a schematic illustration of a computer system and a receiverthat are used as part of the object identification system.

DETAILED DESCRIPTION 1. Surface-Guided Transmission Line Devices andSignal Generation

To begin, some terminology shall be established to provide clarity inthe discussion of concepts to follow. First, as contemplated herein, aformal distinction is drawn between radiated electromagnetic fields andguided electromagnetic fields.

As contemplated herein, a radiated electromagnetic field compriseselectromagnetic energy that is emitted from a source structure in theform of waves that are not bound to a waveguide. For example, a radiatedelectromagnetic field is generally a field that leaves an electricstructure such as an antenna and propagates through the atmosphere orother medium and is not bound to any waveguide structure. Once radiatedelectromagnetic waves leave an electric structure such as an antenna,they continue to propagate in the medium of propagation (such as air)independent of their source until they dissipate regardless of whetherthe source continues to operate. Once electromagnetic waves areradiated, they are not recoverable unless intercepted, and, if notintercepted, the energy inherent in the radiated electromagnetic wavesis lost forever. Electrical structures such as antennas are designed toradiate electromagnetic fields by maximizing the ratio of the radiationresistance to the structure loss resistance. Radiated energy spreads outin space and is lost regardless of whether a receiver is present. Theenergy density of the radiated fields is a function of distance due togeometric spreading. Accordingly, the term “radiate” in all its forms asused herein refers to this form of electromagnetic propagation.

A guided electromagnetic field is a propagating electromagnetic wavewhose energy is concentrated within or near boundaries between mediahaving different electromagnetic properties. In this sense, a guidedelectromagnetic field is one that is bound to a waveguide and may becharacterized as being conveyed by the current flowing in the waveguide.If there is no load to receive and/or dissipate the energy conveyed in aguided electromagnetic wave, then no energy is lost except for thatdissipated in the conductivity of the guiding medium. Stated anotherway, if there is no load for a guided electromagnetic wave, then noenergy is consumed. Thus, a generator or other source generating aguided electromagnetic field does not deliver real power unless aresistive load is present. To this end, such a generator or other sourceessentially runs idle until a load is presented. This is akin to runninga generator to generate a 60 Hertz electromagnetic wave that istransmitted over power lines where there is no electrical load. Itshould be noted that a guided electromagnetic field or wave is theequivalent to what is termed a “transmission line mode.” This contrastswith radiated electromagnetic waves in which real power is supplied atall times in order to generate radiated waves. Unlike radiatedelectromagnetic waves, guided electromagnetic energy does not continueto propagate along a finite length waveguide after the energy source isturned off. Accordingly, the term “guide” in all its forms as usedherein refers to this transmission mode of electromagnetic propagation.

Referring now to FIG. 1, shown is a graph 100 of field strength indecibels (dB) above an arbitrary reference in volts per meter as afunction of distance in kilometers on a log-dB plot to furtherillustrate the distinction between radiated and guided electromagneticfields. The graph 100 of FIG. 1 depicts a guided field strength curve103 that shows the field strength of a guided electromagnetic field as afunction of distance. This guided field strength curve 103 isessentially the same as a transmission line mode. Also, the graph 100 ofFIG. 1 depicts a radiated field strength curve 106 that shows the fieldstrength of a radiated electromagnetic field as a function of distance.

Of interest are the shapes of the curves 103 and 106 for guided wave andfor radiation propagation, respectively. The radiated field strengthcurve 106 falls off geometrically (1/d, where d is distance), which isdepicted as a straight line on the log-log scale. The guided fieldstrength curve 103, on the other hand, has a characteristic exponentialdecay of e^(−αd)/√{square root over (d)} and exhibits a distinctive knee109 on the log-log scale. The guided field strength curve 103 and theradiated field strength curve 106 intersect at point 112, which occursat a crossing distance. At distances less than the crossing distance atintersection point 112, the field strength of a guided electromagneticfield is significantly greater at most locations than the field strengthof a radiated electromagnetic field. At distances greater than thecrossing distance, the opposite is true. Thus, the guided and radiatedfield strength curves 103 and 106 further illustrate the fundamentalpropagation difference between guided and radiated electromagneticfields. For an informal discussion of the difference between guided andradiated electromagnetic fields, reference is made to Milligan, T.,Modern Antenna Design, McGraw-Hill, 1^(st) Edition, 1985, pp. 8-9, whichis incorporated herein by reference in its entirety.

The distinction between radiated and guided electromagnetic waves, madeabove, is readily expressed formally and placed on a rigorous basis.That two such diverse solutions could emerge from one and the samelinear partial differential equation, the wave equation, analyticallyfollows from the boundary conditions imposed on the problem. The Greenfunction for the wave equation, itself, contains the distinction betweenthe nature of radiation and guided waves.

In empty space, the wave equation is a differential operator whoseeigenfunctions possess a continuous spectrum of eigenvalues on thecomplex wave-number plane. This transverse electro-magnetic (TEM) fieldis called the radiation field, and those propagating fields are called“Hertzian waves.” However, in the presence of a conducting boundary, thewave equation plus boundary conditions mathematically lead to a spectralrepresentation of wave-numbers composed of a continuous spectrum plus asum of discrete spectra. To this end, reference is made to Sommerfeld,A., “Uber die Ausbreitung der Wellen in der Drahtlosen Telegraphie,”Annalen der Physik, Vol. 28, 1909, pp. 665-736. Also see Sommerfeld, A.,“Problems of Radio,” published as Chapter 6 in Partial DifferentialEquations in Physics-Lectures on Theoretical Physics: Volume VI,Academic Press, 1949, pp. 236-289, 295-296; Collin, R. E., “HertzianDipole Radiating Over a Lossy Earth or Sea: Some Early and Late 20^(th)Century Controversies,” IEEE Antennas and Propaaation Magazine, Vol. 46,No. 2, April 2004, pp. 64-79; and Reich, H. J., Ordnung, P. F, Krauss,H. L., and Skalnik, J. G., Microwave Theory and Technioues, VanNostrand, 1953, pp. 291-293, each of these references being incorporatedherein by reference in its entirety.

The terms “ground wave” and “surface wave” identify two distinctlydifferent physical propagation phenomena. A surface wave arisesanalytically from a distinct pole yielding a discrete component in theplane wave spectrum. See, e.g., “The Excitation of Plane Surface Waves”by Cullen, A. L., (Proceedings of the IEE (British), Vol. 101, Part IV,August 1954, pp. 225-235). In this context, a surface wave is consideredto be a guided surface wave. The surface wave (in the Zenneck-Sommerfeldguided wave sense) is, physically and mathematically, not the same asthe ground wave (in the Weyl-Norton-FCC sense) that is now so familiarfrom radio broadcasting. These two propagation mechanisms arise from theexcitation of different types of eigenvalue spectra (continuum ordiscrete) on the complex plane. The field strength of the guided surfacewave decays exponentially with distance as illustrated by curve 103 ofFIG. 1 (much like propagation in a lossy waveguide) and resemblespropagation in a radial transmission line, as opposed to the classicalHertzian radiation of the ground wave, which propagates spherically,possesses a continuum of eigenvalues, falls off geometrically asillustrated by curve 106 of FIG. 1, and results from branch-cutintegrals. As experimentally demonstrated by C. R. Burrows in “TheSurface Wave in Radio Propagation over Plane Earth” (Proceedings of theIRE, Vol. 25, No. 2, February, 1937, pp. 219-229) and “The Surface Wavein Radio Transmission” (Bell Laboratories Record, Vol. 15, June 1937,pp. 321-324), vertical antennas radiate ground waves but do not launchguided surface waves.

To summarize the above, first, the continuous part of the wave-numbereigenvalue spectrum, corresponding to branch-cut integrals, produces theradiation field, and second, the discrete spectra, and correspondingresidue sum arising from the poles enclosed by the contour ofintegration, result in non-TEM traveling surface waves that areexponentially damped in the direction transverse to the propagation.Such surface waves are guided transmission line modes. For furtherexplanation, reference is made to Friedman, B., Principles andTechniques of Applied Mathematics, Wiley, 1956, pp. pp. 214, 283-286,290, 298-300.

In free space, antennas excite the continuum eigenvalues of the waveequation, which is a radiation field, where the outwardly propagating RFenergy with E_(z) and H_(Φ) in-phase is lost forever. On the other hand,waveguide probes excite discrete eigenvalues, which results intransmission line propagation. See Collin, R. E., Field Theory of GuidedWaves, McGraw-Hill, 1960, pp. 453, 474-477. While such theoreticalanalyses have held out the hypothetical possibility of launching opensurface guided waves over planar or spherical surfaces of lossy,homogeneous media, for more than a century no known structures in theengineering arts have existed for accomplishing this with any practicalefficiency. Unfortunately, since it emerged in the early 1900's, thetheoretical analysis set forth above has essentially remained a theoryand there have been no known structures for practically accomplishingthe launching of open surface guided waves over planar or sphericalsurfaces of lossy, homogeneous media.

According to the various embodiments of the present disclosure, variousguided surface waveguide probes are described that are configured toexcite electric fields that couple into a guided surface waveguide modealong the surface of a lossy conducting medium. Such guidedelectromagnetic fields are substantially mode-matched in magnitude andphase to a guided surface wave mode on the surface of the lossyconducting medium. Such a guided surface wave mode can also be termed aZenneck waveguide mode. By virtue of the fact that the resultant fieldsexcited by the guided surface waveguide probes described herein aresubstantially mode-matched to a guided surface waveguide mode on thesurface of the lossy conducting medium, a guided electromagnetic fieldin the form of a guided surface wave is launched along the surface ofthe lossy conducting medium. According to one embodiment, the lossyconducting medium comprises a terrestrial medium such as the Earth.

Referring to FIG. 2, shown is a propagation interface that provides foran examination of the boundary value solutions to Maxwell's equationsderived in 1907 by Jonathan Zenneck as set forth in his paper Zenneck,J., “On the Propagation of Plane Electromagnetic Waves Along a FlatConducting Surface and their Relation to Wireless Telegraphy,” Annalender Physik, Serial 4, Vol. 23, Sep. 20, 1907, pp. 846-866. FIG. 2depicts cylindrical coordinates for radially propagating waves along theinterface between a lossy conducting medium specified as Region 1 and aninsulator specified as Region 2. Region 1 can comprise, for example, anylossy conducting medium. In one example, such a lossy conducting mediumcan comprise a terrestrial medium such as the Earth or other medium.Region 2 is a second medium that shares a boundary interface with Region1 and has different constitutive parameters relative to Region 1. Region2 can comprise, for example, any insulator such as the atmosphere orother medium. The reflection coefficient for such a boundary interfacegoes to zero only for incidence at a complex Brewster angle. SeeStratton, J. A., Electromagnetic Theory, McGraw-Hill, 1941, p. 516.

According to various embodiments, the present disclosure sets forthvarious guided surface waveguide probes that generate electromagneticfields that are substantially mode-matched to a guided surface waveguidemode on the surface of the lossy conducting medium comprising Region 1.According to various embodiments, such electromagnetic fieldssubstantially synthesize a wave front incident at a complex Brewsterangle of the lossy conducting medium that can result in zero reflection.

To explain further, in Region 2, where an e^(jωt) field variation isassumed and where ρ≠0 andz≥0 (with z being the vertical coordinatenormal to the surface of Region 1, and ρ being the radial dimension incylindrical coordinates), Zenneck's closed-form exact solution ofMaxwell's equations satisfying the boundary conditions along theinterface are expressed by the following electric field and magneticfield components:

$\begin{matrix}{{H_{2\; \varphi} = {{Ae}^{{- u_{2}}z}{H_{1}^{(2)}( {{- j}\; \gamma \; \rho} )}}},} & (1) \\{{E_{2\; \rho} = {{A( \frac{u_{2}}{j\; \omega \; ɛ_{0}} )}e^{{- u_{2}}z}{H_{1}^{(2)}( {{- j}\; \gamma \; \rho} )}}},{and}} & (2) \\{E_{2z} = {{A( \frac{- \gamma}{\omega \; ɛ_{0}} )}e^{{- u_{2}}z}{{H_{0}^{(2)}( {{- j}\; \gamma \; \rho} )}.}}} & (3)\end{matrix}$

In Region 1, where the e^(jωt) field variation is assumed and where ρ≠0and z≤0, Zenneck's closed-form exact solution of Maxwell's equationssatisfying the boundary conditions along the interface is expressed bythe following electric field and magnetic field components:

$\begin{matrix}{{H_{1\; \varphi} = {{Ae}^{u_{1}z}{H_{1}^{(2)}( {{- j}\; \gamma \; \rho} )}}},} & (4) \\{{E_{1\; \rho} = {{A( \frac{u_{2}}{\sigma_{1} + {j\; \omega \; ɛ_{1}}} )}e^{u_{1}z}{H_{1}^{(2)}( {{- j}\; \gamma \; \rho} )}}},{and}} & (5) \\{E_{1z} = {{A( \frac{- \gamma}{\sigma_{1} + {j\; \omega \; ɛ_{1}}} )}e^{u_{1}z}{{H_{0}^{(2)}( {{- j}\; \gamma \; \rho} )}.}}} & (6)\end{matrix}$

In these expressions, z is the vertical coordinate normal to the surfaceof Region 1 and ρ is the radial coordinate, H_(n) ⁽²⁾(−jγρ) is a complexargument Hankel function of the second kind and order n, u₁ is thepropagation constant in the positive vertical (z) direction in Region 1,u₂ is the propagation constant in the vertical (z) direction in Region2, σ₁ is the conductivity of Region 1, ω is equal to 2πf, where f is afrequency of excitation, ε₀ is the permittivity of free space, ε₁ is thepermittivity of Region 1, A is a source constant imposed by the source,and γ is a surface wave radial propagation constant.

The propagation constants in the ±z directions are determined byseparating the wave equation above and below the interface betweenRegions 1 and 2, and imposing the boundary conditions. This exercisegives, in Region 2,

$\begin{matrix}{u_{2} = \frac{- {jk}_{0}}{\sqrt{1 + ( {ɛ_{r} - {jx}} )}}} & (7)\end{matrix}$

and gives, in Region 1,

u ₁ =−u ₂(ε_(r) −jx).  (8)

The radial propagation constant γ is given by

$\begin{matrix}{{\gamma = {{j\sqrt{k_{0}^{2} + u_{2}^{2}}} = {j\frac{k_{o}n}{\sqrt{1 + n^{2}}}}}},} & (9)\end{matrix}$

which is a complex expression where n is the complex index of refractiongiven by

n=ε _(r) −jx.  (10)

In all of the above Equations,

$\begin{matrix}{{x = \frac{\sigma_{1}}{\omega \; ɛ_{o}}},{and}} & (11) \\{{k_{o} = {{\omega \sqrt{\mu_{o}ɛ_{o}}} = \frac{\lambda_{0}}{2\; \pi}}},} & (12)\end{matrix}$

where ε_(r) comprises the relative permittivity of Region 1, σ₁ is theconductivity of Region 1, ε₀ is the permittivity of free space, and μ₀comprises the permeability of free space. Thus, the generated surfacewave propagates parallel to the interface and exponentially decaysvertical to it. This is known as evanescence.

Thus, Equations (1)-(3) can be considered to be acylindrically-symmetric, radially-propagating waveguide mode. SeeBarlow, H. M., and Brown, J., Radio Surface Waves, Oxford UniversityPress, 1962, pp. 10-12, 29-33. The present disclosure details structuresthat excite this “open boundary” waveguide mode. Specifically, accordingto various embodiments, a guided surface waveguide probe is providedwith a charge terminal of appropriate size that is fed with voltageand/or current and is positioned relative to the boundary interfacebetween Region 2 and Region 1. This may be better understood withreference to FIG. 3, which shows an example of a guided surfacewaveguide probe 200 a that includes a charge terminal T₁ elevated abovea lossy conducting medium 203 (e.g., the Earth) along a vertical axis zthat is normal to a plane presented by the lossy conducting medium 203.The lossy conducting medium 203 makes up Region 1, and a second medium206 makes up Region 2 and shares a boundary interface with the lossyconducting medium 203.

According to one embodiment, the lossy conducting medium 203 cancomprise a terrestrial medium such as the planet Earth. To this end,such a terrestrial medium comprises all structures or formationsincluded thereon whether natural or man-made. For example, such aterrestrial medium can comprise natural elements such as rock, soil,sand, fresh water, sea water, trees, vegetation, and all other naturalelements that make up our planet. In addition, such a terrestrial mediumcan comprise man-made elements such as concrete, asphalt, buildingmaterials, and other man-made materials. In other embodiments, the lossyconducting medium 203 can comprise some medium other than the Earth,whether naturally occurring or man-made. In other embodiments, the lossyconducting medium 203 can comprise other media such as man-made surfacesand structures such as automobiles, aircraft, man-made materials (suchas plywood, plastic sheeting, or other materials) or other media.

In the case where the lossy conducting medium 203 comprises aterrestrial medium or Earth, the second medium 206 can comprise theatmosphere above the ground. As such, the atmosphere can be termed an“atmospheric medium” that comprises air and other elements that make upthe atmosphere of the Earth. In addition, it is possible that the secondmedium 206 can comprise other media relative to the lossy conductingmedium 203.

The guided surface waveguide probe 200 a includes a feed network 209that couples an excitation source 212 to the charge terminal T₁ via,e.g., a vertical feed line conductor. According to various embodiments,a charge Q₁ is imposed on the charge terminal T₁ to synthesize anelectric field based upon the voltage applied to terminal T₁ at anygiven instant. Depending on the angle of incidence (θ_(i)) of theelectric field (E), it is possible to substantially mode-match theelectric field to a guided surface waveguide mode on the surface of thelossy conducting medium 203 comprising Region 1.

By considering the Zenneck closed-form solutions of Equations (1)-(6),the Leontovich impedance boundary condition between Region 1 and Region2 can be stated as

{circumflex over (z)}×

₂(ρ,φ,0)=

_(S),  (13)

where {circumflex over (z)} is a unit normal in the positive vertical(+z) direction and

₂ is the magnetic field strength in Region 2 expressed by Equation (1)above. Equation (13) implies that the electric and magnetic fieldsspecified in Equations (1)-(3) may result in a radial surface currentdensity along the boundary interface, where the radial surface currentdensity can be specified by

Jρ(ρ′)=−A H ₁ ⁽²⁾(−jγρ′)  (14)

where A is a constant. Further, it should be noted that close-in to theguided surface waveguide probe 200 (for ρ<<λ), Equation (14) above hasthe behavior

$\begin{matrix}{{J_{close}( \rho^{\prime} )} = {\frac{- {A( {j\; 2} )}}{\pi ( {{- j}\; \gamma \; \rho^{\prime}} )} = {{- H_{\varphi}} = {- {\frac{I_{o}}{2{\pi\rho}^{\prime}}.}}}}} & (15)\end{matrix}$

The negative sign means that when source current (I₀) flows verticallyupward as illustrated in FIG. 3, the “close-in” ground current flowsradially inward. By field matching on H_(ϕ) “close-in,” it can bedetermined that

$\begin{matrix}{A = {{- \frac{I_{o}\gamma}{4}} = {- \frac{\omega \; q_{1}\gamma}{4}}}} & (16)\end{matrix}$

where q₁=C₁V₁, in Equations (1)-(6) and (14). Therefore, the radialsurface current density of Equation (14) can be restated as

$\begin{matrix}{{J_{\rho}( \rho^{\prime} )} = {\frac{I_{o}\gamma}{4}\mspace{11mu} {{H_{1}^{(2)}( {{- j}\; {\gamma\rho}^{\prime}} )}.}}} & (17)\end{matrix}$

The fields expressed by Equations (1)-(6) and (17) have the nature of atransmission line mode bound to a lossy interface, not radiation fieldsthat are associated with groundwave propagation. See Barlow, H. M. andBrown, J., Radio Surface Waves, Oxford University Press, 1962, pp. 1-5.

At this point, a review of the nature of the Hankel functions used inEquations (1)-(6) and (17) is provided for these solutions of the waveequation. One might observe that the Hankel functions of the first andsecond kind and order n are defined as complex combinations of thestandard Bessel functions of the first and second kinds

H _(n) ⁽¹⁾(x)=J _(n)(x)+jN _(n)(x), and  (18)

H _(n) ⁽²⁾(x)=J _(n)(x)−jN _(n)(x),  (19)

These functions represent cylindrical waves propagating radially inward(H_(n) ⁽¹⁾) and outward (H_(n) ⁽²⁾), respectively. The definition isanalogous to the relationship e^(±jx)=cos x±j sin x. See, for example,Harrington, R. F., Time-Harmonic Fields, McGraw-Hill, 1961, pp. 460-463.

That H_(n) ⁽²⁾(k_(ρ)ρ) is an outgoing wave can be recognized from itslarge argument asymptotic behavior that is obtained directly from theseries definitions of J_(n)(x) and N_(n)(x). Far-out from the guidedsurface waveguide probe:

$\begin{matrix}{{{{H_{n}^{(2)}(x)}\underset{xarrow\infty}{arrow}{\sqrt{\frac{2j}{\pi \; x}}j^{n}e^{- {jx}}}} = {\sqrt{\frac{2}{\pi \; x}}j^{n}e^{- {j{({x - \frac{\pi}{4}})}}}}},} & ( {20a} )\end{matrix}$

which, when multiplied by e^(jωt), is an outward propagating cylindricalwave of the form e^(j(ωt-kρ)) with a 1/√{square root over (ρ)} spatialvariation. The first order (n=1) solution can be determined fromEquation (20a) to be

$\begin{matrix}{{{H_{1}^{(2)}(x)}\underset{xarrow\infty}{arrow}{j\sqrt{\frac{2j}{\pi \; x}}e^{- {jx}}}} = {\sqrt{\frac{2}{\pi \; x}}{e^{- {j{({x - \frac{\pi}{2} - \frac{\pi}{4}})}}}.}}} & ( {20b} )\end{matrix}$

Close-in to the guided surface waveguide probe (for ρ<<λ), the Hankelfunction of first order and the second kind behaves as

$\begin{matrix}{{H_{1}^{(2)}(x)}\underset{xarrow 0}{arrow}{\frac{2j}{\pi \; x}.}} & (21)\end{matrix}$

Note that these asymptotic expressions are complex quantities. When x isa real quantity, Equations (20b) and (21) differ in phase by √{squareroot over (j)}, which corresponds to an extra phase advance or “phaseboost” of 45° or, equivalently, λ/8. The close-in and far-out asymptotesof the first order Hankel function of the second kind have a Hankel“crossover” or transition point where they are of equal magnitude at adistance of ρ=R_(x).

Thus, beyond the Hankel crossover point the “far out” representationpredominates over the “close-in” representation of the Hankel function.The distance to the Hankel crossover point (or Hankel crossoverdistance) can be found by equating Equations (20b) and (21) for −jγρ,and solving for R_(x). With x=σ/ωε₀, it can be seen that the far-out andclose-in Hankel function asymptotes are frequency dependent, with theHankel crossover point moving out as the frequency is lowered. It shouldalso be noted that the Hankel function asymptotes may also vary as theconductivity (σ) of the lossy conducting medium changes. For example,the conductivity of the soil can vary with changes in weatherconditions.

Referring to FIG. 4, shown is an example of a plot of the magnitudes ofthe first order Hankel functions of Equations (20b) and (21) for aRegion 1 conductivity of σ=0.010 mhos/m and relative permittivityε_(r)=15, at an operating frequency of 1850 kHz. Curve 115 is themagnitude of the far-out asymptote of Equation (20b) and curve 118 isthe magnitude of the close-in asymptote of Equation (21), with theHankel crossover point 121 occurring at a distance of R_(x)=54 feet.While the magnitudes are equal, a phase offset exists between the twoasymptotes at the Hankel crossover point 121. It can also be seen thatthe Hankel crossover distance is much less than a wavelength of theoperation frequency.

Considering the electric field components given by Equations (2) and (3)of the Zenneck closed-form solution in Region 2, it can be seen that theratio of E_(z) and E_(ρ) asymptotically passes to

$\begin{matrix}{{\frac{E_{z}}{E_{\rho}} = {{{( \frac{{- j}\; \gamma}{u_{2}} )\frac{H_{0}^{(2)}( {{- j}\; {\gamma\rho}} )}{H_{1}^{(2)}( {{- j}\; {\gamma\rho}} )}}\underset{\rhoarrow\infty}{arrow}\sqrt{ɛ_{r} - {j\frac{\sigma}{{\omega ɛ}_{o}}}}} = {n = {\tan \mspace{11mu} \theta_{i}}}}},} & (22)\end{matrix}$

where n is the complex index of refraction of Equation (10) and θ_(i) isthe angle of incidence of the electric field. In addition, the verticalcomponent of the mode-matched electric field of Equation (3)asymptotically passes to

$\begin{matrix}{{E_{2z}\underset{\rhoarrow\infty}{arrow}{( \frac{q_{free}}{ɛ_{o}} )\sqrt{\frac{\gamma^{3}}{8\pi}}e^{{- u_{2}}z}\frac{e^{- {j{({{\gamma\rho} - {\pi/4}})}}}}{\sqrt{\rho}}}},} & (23)\end{matrix}$

which is linearly proportional to free charge on the isolated componentof the elevated charge terminal's capacitance at the terminal voltage,q_(free)=C_(free)×V_(T).

For example, the height H₁ of the elevated charge terminal T₁ in FIG. 3affects the amount of free charge on the charge terminal T₁. When thecharge terminal T₁ is near the ground plane of Region 1, most of thecharge Q₁ on the terminal is “bound.” As the charge terminal T₁ iselevated, the bound charge is lessened until the charge terminal T₁reaches a height at which substantially all of the isolated charge isfree.

The advantage of an increased capacitive elevation for the chargeterminal T₁ is that the charge on the elevated charge terminal T₁ isfurther removed from the ground plane, resulting in an increased amountof free charge q_(free) to couple energy into the guided surfacewaveguide mode. As the charge terminal T₁ is moved away from the groundplane, the charge distribution becomes more uniformly distributed aboutthe surface of the terminal. The amount of free charge is related to theself-capacitance of the charge terminal T₁.

For example, the capacitance of a spherical terminal can be expressed asa function of physical height above the ground plane. The capacitance ofa sphere at a physical height of h above a perfect ground is given by

C _(elevated sphere)=4πε₀ a(1+M+M ² +M ³+2M′+3M ⁵+ . . . ),  (24)

where the diameter of the sphere is 2a, and where M=a/2h with h beingthe height of the spherical terminal. As can be seen, an increase in theterminal height h reduces the capacitance C of the charge terminal. Itcan be shown that for elevations of the charge terminal T₁ that are at aheight of about four times the diameter (4D=8a) or greater, the chargedistribution is approximately uniform about the spherical terminal,which can improve the coupling into the guided surface waveguide mode.

In the case of a sufficiently isolated terminal, the self-capacitance ofa conductive sphere can be approximated by C=4πε₀a, where a is theradius of the sphere in meters, and the self-capacitance of a disk canbe approximated by C=8ε₀a, where a is the radius of the disk in meters.The charge terminal T₁ can include any shape such as a sphere, a disk, acylinder, a cone, a torus, a hood, one or more rings, or any otherrandomized shape or combination of shapes. An equivalent sphericaldiameter can be determined and used for positioning of the chargeterminal T₁.

This may be further understood with reference to the example of FIG. 3,where the charge terminal T₁ is elevated at a physical height ofh_(p)=H₁ above the lossy conducting medium 203. To reduce the effects ofthe “bound” charge, the charge terminal T₁ can be positioned at aphysical height that is at least four times the spherical diameter (orequivalent spherical diameter) of the charge terminal T₁ to reduce thebounded charge effects.

Referring next to FIG. 5A, shown is a ray optics interpretation of theelectric field produced by the elevated charge Q₁ on charge terminal T₁of FIG. 3. As in optics, minimizing the reflection of the incidentelectric field can improve and/or maximize the energy coupled into theguided surface waveguide mode of the lossy conducting medium 203. For anelectric field (ε_(∥)) that is polarized parallel to the plane ofincidence (not the boundary interface), the amount of reflection of theincident electric field may be determined using the Fresnel reflectioncoefficient, which can be expressed as

$\begin{matrix}{{{\Gamma_{}( \theta_{i} )} = {\frac{E_{{,R}}}{E_{{,i}}} = \frac{\sqrt{( {ɛ_{r} - {jx}} ) - {\sin^{2}\theta_{i}}} - {( {ɛ_{r} - {jx}} )\mspace{11mu} \cos \mspace{11mu} \theta_{i}}}{\sqrt{( {ɛ_{r} - {jx}} ) - {\sin^{2}\theta_{i}}} + {( {ɛ_{r} - {jx}} )\mspace{11mu} \cos \mspace{11mu} \theta_{i}}}}},} & (25)\end{matrix}$

where θ_(i) is the conventional angle of incidence measured with respectto the surface normal.

In the example of FIG. 5A, the ray optic interpretation shows theincident field polarized parallel to the plane of incidence having anangle of incidence of θ_(i), which is measured with respect to thesurface normal ({circumflex over (z)}). There will be no reflection ofthe incident electric field when Γ_(∥)(θ_(i))=0 and thus the incidentelectric field will be completely coupled into a guided surfacewaveguide mode along the surface of the lossy conducting medium 203. Itcan be seen that the numerator of Equation (25) goes to zero when theangle of incidence is

θ_(i)=arctan(√{square root over (ε_(r) −jx)})=θ_(i,B),  (26)

where x=σ/ωε₀. This complex angle of incidence (θ_(i,B)) is referred toas the Brewster angle. Referring back to Equation (22), it can be seenthat the same complex Brewster angle (θ_(i,B)) relationship is presentin both Equations (22) and (26).

As illustrated in FIG. 5A, the electric field vector E can be depictedas an incoming non-uniform plane wave, polarized parallel to the planeof incidence. The electric field vector E can be created fromindependent horizontal and vertical components as

=(θ_(i))=E _(ρ) {circumflex over (ρ)}+E _(z) {circumflex over(z)}.  (27)

Geometrically, the illustration in FIG. 5A suggests that the electricfield vector E can be given by

$\begin{matrix}{{{E_{\rho}( {\rho,z} )} = {{E( {\rho,z} )}\mspace{11mu} \cos \mspace{11mu} \theta_{i}}},{and}} & ( {28a} ) \\{{{E_{z}( {\rho,z} )} = {{{E( {\rho,z} )}\mspace{11mu} \cos \mspace{11mu} ( {\frac{\pi}{2} - \theta_{i}} )} = {{E( {\rho,z} )}\mspace{11mu} \sin \mspace{11mu} \theta_{i}}}},} & ( {28b} )\end{matrix}$

which means that the field ratio is

$\begin{matrix}{\frac{E_{\rho}}{E_{z}} = {\frac{1}{\tan \mspace{11mu} \theta_{i}} = {\tan \mspace{11mu} {\psi_{i}.}}}} & (29)\end{matrix}$

A generalized parameter W, called “wave tilt,” is noted herein as theratio of the horizontal electric field component to the verticalelectric field component given by

$\begin{matrix}{{W = {\frac{E_{\rho}}{E_{z}} = {{W}e^{j\; \Psi}}}},{or}} & ( {30a} ) \\{{\frac{1}{W} = {\frac{E_{z}}{E_{\rho}} = {{\tan \mspace{11mu} \theta_{i}} = {\frac{1}{W}e^{{- j}\; \Psi}}}}},} & ( {30b} )\end{matrix}$

which is complex and has both magnitude and phase. For anelectromagnetic wave in Region 2, the wave tilt angle (Ψ) is equal tothe angle between the normal of the wave-front at the boundary interfacewith Region 1 and the tangent to the boundary interface. This may beeasier to see in FIG. 5B, which illustrates equi-phase surfaces of anelectromagnetic wave and their normals for a radial cylindrical guidedsurface wave. At the boundary interface (z=0) with a perfect conductor,the wave-front normal is parallel to the tangent of the boundaryinterface, resulting in W=0. However, in the case of a lossy dielectric,a wave tilt W exists because the wave-front normal is not parallel withthe tangent of the boundary interface at z=0.

Applying Equation (30b) to a guided surface wave gives

$\begin{matrix}{{\tan \mspace{11mu} \theta_{i,B}} = {\frac{E_{z}}{E_{\rho}} = {\frac{u_{2}}{\gamma} = {\sqrt{ɛ_{r} - {jx}} = {n = {\frac{1}{W} = {\frac{1}{W}{e^{{- j}\; \Psi}.}}}}}}}} & (31)\end{matrix}$

With the angle of incidence equal to the complex Brewster angle(θ_(i,B)), the Fresnel reflection coefficient of Equation (25) vanishes,as shown by

$\begin{matrix}{{{{\Gamma_{}( \theta_{i,B} )} = \frac{\sqrt{( {ɛ_{r} - {jx}} ) - {\sin^{2}\theta_{i}}} - {( {ɛ_{r} - {jx}} )\mspace{11mu} \cos \mspace{11mu} \theta_{i}}}{\sqrt{( {ɛ_{r} - {jx}} ) - {\sin^{2}\theta_{i}}} + {( {ɛ_{r} - {jx}} )\mspace{11mu} \cos \mspace{11mu} \theta_{i}}}}}_{\theta_{i} = \theta_{i,B}} = 0.} & (32)\end{matrix}$

By adjusting the complex field ratio of Equation (22), an incident fieldcan be synthesized to be incident at a complex angle at which thereflection is reduced or eliminated. Establishing this ratio asn=√{square root over (ε_(r)−jx)} results in the synthesized electricfield being incident at the complex Brewster angle, making thereflections vanish.

The concept of an electrical effective height can provide furtherinsight into synthesizing an electric field with a complex angle ofincidence with a guided surface waveguide probe 200. The electricaleffective height (h_(eff)) has been defined as

$\begin{matrix}{h_{eff} = {\frac{1}{I_{0}}{\int_{0}^{h_{p}}{{I(z)}{dz}}}}} & (33)\end{matrix}$

for a monopole with a physical height (or length) of h_(p). Since theexpression depends upon the magnitude and phase of the sourcedistribution along the structure, the effective height (or length) iscomplex in general. The integration of the distributed current I(z) ofthe structure is performed over the physical height of the structure(h_(p)), and normalized to the ground current (I₀) flowing upwardthrough the base (or input) of the structure. The distributed currentalong the structure can be expressed by

I(z)=I _(C) cos(β₀ z),  (34)

where β₀ is the propagation factor for current propagating on thestructure. In the example of FIG. 3, I_(C) is the current that isdistributed along the vertical structure of the guided surface waveguideprobe 200 a.

For example, consider a feed network 209 that includes a low loss coil(e.g., a helical coil) at the bottom of the structure and a verticalfeed line conductor connected between the coil and the charge terminalT₁. The phase delay due to the coil (or helical delay line) isθ_(c)=β_(p)l_(C), with a physical length of l_(C) and a propagationfactor of

$\begin{matrix}{{\beta_{p} = {\frac{2\pi}{\lambda_{p}} = \frac{2\pi}{V_{f}\lambda_{0}}}},} & (35)\end{matrix}$

where V_(f) is the velocity factor on the structure, λ₀ is thewavelength at the supplied frequency, and λ_(p) is the propagationwavelength resulting from the velocity factor V_(f). The phase delay ismeasured relative to the ground (stake) current I₀.

In addition, the spatial phase delay along the length l_(w) of thevertical feed line conductor can be given by θ_(y)=β_(w)l_(w) whereβ_(w) is the propagation phase constant for the vertical feed lineconductor. In some implementations, the spatial phase delay may beapproximated by θ_(y)=β_(w)h_(p), since the difference between thephysical height h_(p) of the guided surface waveguide probe 200 a andthe vertical feed line conductor length l_(w) is much less than awavelength at the supplied frequency (λ₀). As a result, the total phasedelay through the coil and vertical feed line conductor isΦ=θ_(c)+θ_(y), and the current fed to the top of the coil from thebottom of the physical structure is

I _(C)(θ_(c)+θ_(y))=I ₀ e ^(jΦ),  (36)

with the total phase delay Φ measured relative to the ground (stake)current I₀. Consequently, the electrical effective height of a guidedsurface waveguide probe 200 can be approximated by

$\begin{matrix}{{h_{eff} = {{\frac{1}{I_{0}}{\int_{0}^{h_{p}}{I_{0}e^{j\; \Phi}{\cos ( {\beta_{0}z} )}{dz}}}} \cong {h_{p}e^{j\; \Phi}}}},} & (37)\end{matrix}$

for the case where the physical height h_(p)<<λ₀. The complex effectiveheight of a monopole, h_(eff)=h_(p) at an angle (or phase shift) of Φ,may be adjusted to cause the source fields to match a guided surfacewaveguide mode and cause a guided surface wave to be launched on thelossy conducting medium 203.

In the example of FIG. 5A, ray optics are used to illustrate the complexangle trigonometry of the incident electric field (E) having a complexBrewster angle of incidence (θ_(i,B)) at the Hankel crossover distance(R_(x)) 121. Recall from Equation (26) that, for a lossy conductingmedium, the Brewster angle is complex and specified by

$\begin{matrix}{{\tan \mspace{11mu} \theta_{i,B}} = {\sqrt{ɛ_{r} - {j\frac{\sigma}{{\omega ɛ}_{o}}}} = {n.}}} & (38)\end{matrix}$

Electrically, the geometric parameters are related by the electricaleffective height (h_(eff)) of the charge terminal T₁ by

R _(x) tan ψ_(i,B) =R _(x) ×W=h _(eff) =h _(p) e ^(jΦ),  (39)

where ψ_(i,B)=(π/2)−θ_(i,B) is the Brewster angle measured from thesurface of the lossy conducting medium. To couple into the guidedsurface waveguide mode, the wave tilt of the electric field at theHankel crossover distance can be expressed as the ratio of theelectrical effective height and the Hankel crossover distance

$\begin{matrix}{\frac{h_{eff}}{R_{x}} = {{\tan \mspace{11mu} \psi_{i,B}} = {W_{Rx}.}}} & (40)\end{matrix}$

Since both the physical height (h_(p)) and the Hankel crossover distance(R_(x)) are real quantities, the angle (Ψ) of the desired guided surfacewave tilt at the Hankel crossover distance (R_(x)) is equal to the phase(Φ) of the complex effective height (h_(eff)). This implies that byvarying the phase at the supply point of the coil, and thus the phaseshift in Equation (37), the phase, Φ, of the complex effective heightcan be manipulated to match the angle of the wave tilt, Ψ, of the guidedsurface waveguide mode at the Hankel crossover point 121: Φ=Ψ.

In FIG. 5A, a right triangle is depicted having an adjacent side oflength R_(x) along the lossy conducting medium surface and a complexBrewster angle ψ_(i,B) measured between a ray 124 extending between theHankel crossover point 121 at R_(x) and the center of the chargeterminal T₁, and the lossy conducting medium surface 127 between theHankel crossover point 121 and the charge terminal T₁. With the chargeterminal T₁ positioned at physical height h_(p) and excited with acharge having the appropriate phase delay Φ, the resulting electricfield is incident with the lossy conducting medium boundary interface atthe Hankel crossover distance R_(x), and at the Brewster angle. Underthese conditions, the guided surface waveguide mode can be excitedwithout reflection or substantially negligible reflection.

If the physical height of the charge terminal T₁ is decreased withoutchanging the phase shift D of the effective height (h_(eff)), theresulting electric field intersects the lossy conducting medium 203 atthe Brewster angle at a reduced distance from the guided surfacewaveguide probe 200. FIG. 6 graphically illustrates the effect ofdecreasing the physical height of the charge terminal T₁ on the distancewhere the electric field is incident at the Brewster angle. As theheight is decreased from h₃ through h₂ to h₁, the point where theelectric field intersects with the lossy conducting medium (e.g., theEarth) at the Brewster angle moves closer to the charge terminalposition. However, as Equation (39) indicates, the height H₁ (FIG. 3) ofthe charge terminal T₁ should be at or higher than the physical height(h_(p)) in order to excite the far-out component of the Hankel function.With the charge terminal T₁ positioned at or above the effective height(h_(eff)), the lossy conducting medium 203 can be illuminated at theBrewster angle of incidence (ψ_(i,B)=(π/2)−θ_(i,B)) at or beyond theHankel crossover distance (R_(x)) 121 as illustrated in FIG. 5A. Toreduce or minimize the bound charge on the charge terminal T₁, theheight should be at least four times the spherical diameter (orequivalent spherical diameter) of the charge terminal T₁ as mentionedabove.

A guided surface waveguide probe 200 can be configured to establish anelectric field having a wave tilt that corresponds to a waveilluminating the surface of the lossy conducting medium 203 at a complexBrewster angle, thereby exciting radial surface currents bysubstantially mode-matching to a guided surface wave mode at (or beyond)the Hankel crossover point 121 at R_(x).

Referring to FIG. 7, shown is a graphical representation of an exampleof a guided surface waveguide probe 200 b that includes a chargeterminal T₁. An AC source 212 acts as the excitation source for thecharge terminal T₁, which is coupled to the guided surface waveguideprobe 200 b through a feed network 209 (FIG. 3) comprising a coil 215such as, e.g., a helical coil. In other implementations, the AC source212 can be inductively coupled to the coil 215 through a primary coil.In some embodiments, an impedance matching network may be included toimprove and/or maximize coupling of the AC source 212 to the coil 215.

As shown in FIG. 7, the guided surface waveguide probe 200 b can includethe upper charge terminal T₁ (e.g., a sphere at height h_(p)) that ispositioned along a vertical axis z that is substantially normal to theplane presented by the lossy conducting medium 203. A second medium 206is located above the lossy conducting medium 203. The charge terminal T₁has a self-capacitance C_(T). During operation, charge Q₁ is imposed onthe terminal T₁ depending on the voltage applied to the terminal T₁ atany given instant.

In the example of FIG. 7, the coil 215 is coupled to a ground stake 218at a first end and to the charge terminal T₁ via a vertical feed lineconductor 221. In some implementations, the coil connection to thecharge terminal T₁ can be adjusted using a tap 224 of the coil 215 asshown in FIG. 7. The coil 215 can be energized at an operating frequencyby the AC source 212 through a tap 227 at a lower portion of the coil215. In other implementations, the AC source 212 can be inductivelycoupled to the coil 215 through a primary coil.

The construction and adjustment of the guided surface waveguide probe200 is based upon various operating conditions, such as the transmissionfrequency, conditions of the lossy conducting medium (e.g., soilconductivity 6 and relative permittivity ε_(r)), and size of the chargeterminal T₁. The index of refraction can be calculated from Equations(10) and (11) as

n=ε _(r) −jx,  (41)

where x=σ/ωε₀ with ω=2πf. The conductivity σ and relative permittivityε_(r) can be determined through test measurements of the lossyconducting medium 203. The complex Brewster angle (θ_(i,B)) measuredfrom the surface normal can also be determined from Equation (26) as

θ_(i,B)=arctan(√{square root over (ε_(r) −jx)}),  (42)

or measured from the surface as shown in FIG. 5A as

$\begin{matrix}{\psi_{i,B} = {\frac{\pi}{2} - {\theta_{i,B}.}}} & (43)\end{matrix}$

The wave tilt at the Hankel crossover distance (W_(Rx)) can also befound using Equation (40).

The Hankel crossover distance can also be found by equating themagnitudes of Equations (20b) and (21) for −jγρ, and solving for R_(x)as illustrated by FIG. 4. The electrical effective height can then bedetermined from Equation (39) using the Hankel crossover distance andthe complex Brewster angle as

h _(eff) =h _(p) e ^(jΦ) =R _(x) tan ψ_(i,B).  (44)

As can be seen from Equation (44), the complex effective height(h_(eff)) includes a magnitude that is associated with the physicalheight (h_(p)) of the charge terminal T₁ and a phase delay (Φ) that isto be associated with the angle (Ψ) of the wave tilt at the Hankelcrossover distance (R_(x)). With these variables and the selected chargeterminal T₁ configuration, it is possible to determine the configurationof a guided surface waveguide probe 200.

With the charge terminal T₁ positioned at or above the physical height(h_(p)), the feed network 209 (FIG. 3) and/or the vertical feed lineconnecting the feed network to the charge terminal T₁ can be adjusted tomatch the phase (Φ) of the charge Q₁ on the charge terminal T₁ to theangle (Ψ) of the wave tilt (W). The size of the charge terminal T₁ canbe chosen to provide a sufficiently large surface for the charge Q,imposed on the terminals. In general, it is desirable to make the chargeterminal T₁ as large as practical. The size of the charge terminal T₁should be large enough to avoid ionization of the surrounding air, whichcan result in electrical discharge or sparking around the chargeterminal.

The phase delay θ_(c), of a helically-wound coil can be determined fromMaxwell's equations as has been discussed by Corum, K. L. and J. F.Corum, “RF Coils, Helical Resonators and Voltage Magnification byCoherent Spatial Modes,” Microwave Review, Vol. 7, No. 2, September2001, pp. 36-45., which is incorporated herein by reference in itsentirety. For a helical coil with H/D>1, the ratio of the velocity ofpropagation (ν) of a wave along the coil's longitudinal axis to thespeed of light (c), or the “velocity factor,” is given by

$\begin{matrix}{{V_{f} = {\frac{\upsilon}{c} = \frac{1}{\sqrt{1 + {20( \frac{D}{s} )^{2.5}( \frac{D}{\lambda_{o}} )^{0.5}}}}}},} & (45)\end{matrix}$

where H is the axial length of the solenoidal helix, D is the coildiameter, N is the number of turns of the coil, s=H/N is theturn-to-turn spacing (or helix pitch) of the coil, and A, is thefree-space wavelength. Based upon this relationship, the electricallength, or phase delay, of the helical coil is given by

$\begin{matrix}{\theta_{c} = {{\beta_{p}H} = {{\frac{2\pi}{\lambda_{p}}H} = {\frac{2\pi}{V_{f}\lambda_{0}}{H.}}}}} & (46)\end{matrix}$

The principle is the same if the helix is wound spirally or is short andfat, but V_(f) and θ_(c) are easier to obtain by experimentalmeasurement. The expression for the characteristic (wave) impedance of ahelical transmission line has also been derived as

$\begin{matrix}{Z_{c} = {{\frac{60}{V_{f}}\lbrack {{\; {n( \frac{V_{f}\lambda_{0}}{D} )}} - 1.027} \rbrack}.}} & (47)\end{matrix}$

The spatial phase delay θ_(y) of the structure can be determined usingthe traveling wave phase delay of the vertical feed line conductor 221(FIG. 7). The capacitance of a cylindrical vertical conductor above aprefect ground plane can be expressed as

$\begin{matrix}{{C_{A} = {\frac{2{\pi ɛ}_{o}h_{w}}{{\; {n( \frac{h}{a} )}} - 1}{Farads}}},} & (48)\end{matrix}$

where h_(w) is the vertical length (or height) of the conductor and a isthe radius (in mks units). As with the helical coil, the traveling wavephase delay of the vertical feed line conductor can be given by

$\begin{matrix}{{\theta_{y} = {{\beta_{w}h_{w}} = {{\frac{2\pi}{\lambda_{w}}h_{w}} = {\frac{2\pi}{V_{w}\lambda_{0}}h_{w}}}}},} & (49)\end{matrix}$

where β_(w) is the propagation phase constant for the vertical feed lineconductor, h_(w) is the vertical length (or height) of the vertical feedline conductor, V_(w) is the velocity factor on the wire, λ₀ is thewavelength at the supplied frequency, and λ_(w) is the propagationwavelength resulting from the velocity factor V_(w). For a uniformcylindrical conductor, the velocity factor is a constant withV_(w)≈0.94, or in a range from about 0.93 to about 0.98. If the mast isconsidered to be a uniform transmission line, its average characteristicimpedance can be approximated by

$\begin{matrix}{{Z_{w} = {\frac{60}{V_{w}}\lbrack {{\; {n( \frac{h_{w}}{a} )}} - 1} \rbrack}},} & (50)\end{matrix}$

where V_(w)≈0.94 for a uniform cylindrical conductor and α is the radiusof the conductor. An alternative expression that has been employed inamateur radio literature for the characteristic impedance of asingle-wire feed line can be given by

$\begin{matrix}{Z_{w} = {138\mspace{11mu} {{\log( \frac{1.123\mspace{11mu} V_{w}\lambda_{0}}{2\pi \; a} )}.}}} & (51)\end{matrix}$

Equation (51) implies that Z_(w) for a single-wire feeder varies withfrequency. The phase delay can be determined based upon the capacitanceand characteristic impedance.

With a charge terminal T₁ positioned over the lossy conducting medium203 as shown in FIG. 3, the feed network 209 can be adjusted to excitethe charge terminal T₁ with the phase shift (Φ) of the complex effectiveheight (h_(eff)) equal to the angle (Ψ) of the wave tilt at the Hankelcrossover distance, or Φ=Ψ. When this condition is met, the electricfield produced by the charge oscillating Q₁ on the charge terminal T₁ iscoupled into a guided surface waveguide mode traveling along the surfaceof a lossy conducting medium 203. For example, if the Brewster angle(θ_(i,B)), the phase delay (θ_(y)) associated with the vertical feedline conductor 221 (FIG. 7), and the configuration of the coil 215 (FIG.7) are known, then the position of the tap 224 (FIG. 7) can bedetermined and adjusted to impose an oscillating charge Q₁ on the chargeterminal T₁ with phase Φ=Ψ. The position of the tap 224 may be adjustedto maximize coupling the traveling surface waves into the guided surfacewaveguide mode. Excess coil length beyond the position of the tap 224can be removed to reduce the capacitive effects. The vertical wireheight and/or the geometrical parameters of the helical coil may also bevaried.

The coupling to the guided surface waveguide mode on the surface of thelossy conducting medium 203 can be improved and/or optimized by tuningthe guided surface waveguide probe 200 for standing wave resonance withrespect to a complex image plane associated with the charge Q₁ on thecharge terminal T₁. By doing this, the performance of the guided surfacewaveguide probe 200 can be adjusted for increased and/or maximum voltage(and thus charge Q₁) on the charge terminal T₁. Referring back to FIG.3, the effect of the lossy conducting medium 203 in Region 1 can beexamined using image theory analysis.

Physically, an elevated charge Q₁ placed over a perfectly conductingplane attracts the free charge on the perfectly conducting plane, whichthen “piles up” in the region under the elevated charge Q₁. Theresulting distribution of “bound” electricity on the perfectlyconducting plane is similar to a bell-shaped curve. The superposition ofthe potential of the elevated charge Q₁, plus the potential of theinduced “piled up” charge beneath it, forces a zero equipotentialsurface for the perfectly conducting plane. The boundary value problemsolution that describes the fields in the region above the perfectlyconducting plane may be obtained using the classical notion of imagecharges, where the field from the elevated charge is superimposed withthe field from a corresponding “image” charge below the perfectlyconducting plane.

This analysis may also be used with respect to a lossy conducting medium203 by assuming the presence of an effective image charge Q₁′ beneaththe guided surface waveguide probe 200. The effective image charge Q₁′coincides with the charge Q₁ on the charge terminal T₁ about aconducting image ground plane 130, as illustrated in FIG. 3. However,the image charge Q₁′ is not merely located at some real depth and 180°out of phase with the primary source charge Q₁ on the charge terminalT₁, as they would be in the case of a perfect conductor. Rather, thelossy conducting medium 203 (e.g., a terrestrial medium) presents aphase shifted image. That is to say, the image charge Q₁′ is at acomplex depth below the surface (or physical boundary) of the lossyconducting medium 203. For a discussion of complex image depth,reference is made to Wait, J. R., “Complex Image Theory-Revisited,” IEEEAntennas and Propagation Magazine, Vol. 33, No. 4, August 1991, pp.27-29, which is incorporated herein by reference in its entirety.

Instead of the image charge Q₁′ being at a depth that is equal to thephysical height (H₁) of the charge Q₁, the conducting image ground plane130 (representing a perfect conductor) is located at a complex depth ofz=−d/2 and the image charge Q₁′ appears at a complex depth (i.e., the“depth” has both magnitude and phase), given by −D₁=−(d/2+d/2+H₁)≠H₁.For vertically polarized sources over the Earth,

$\begin{matrix}{{d = {{\frac{2\sqrt{\gamma_{e}^{2} + k_{0}^{2}}}{\gamma_{e}^{2}} \approx \frac{2}{\gamma_{e}}} = {{d_{r} + {jd}_{i}} = {{d}{\angle\zeta}}}}},{where}} & (52) \\{{\gamma_{e}^{2} = {{j\; {\omega\mu}_{1}\sigma_{1}} - {\omega^{2}\mu_{1}ɛ_{1}}}},{and}} & (53) \\{{k_{o} = {\omega \sqrt{\mu_{o}ɛ_{o}}}},} & (54)\end{matrix}$

as indicated in Equation (12). The complex spacing of the image charge,in turn, implies that the external field will experience extra phaseshifts not encountered when the interface is either a dielectric or aperfect conductor. In the lossy conducting medium, the wave front normalis parallel to the tangent of the conducting image ground plane 130 atz=−d/2, and not at the boundary interface between Regions 1 and 2.

Consider the case illustrated in FIG. 8A where the lossy conductingmedium 203 is a finitely conducting Earth 133 with a physical boundary136. The finitely conducting Earth 133 may be replaced by a perfectlyconducting image ground plane 139 as shown in FIG. 8B, which is locatedat a complex depth z₁ below the physical boundary 136. This equivalentrepresentation exhibits the same impedance when looking down into theinterface at the physical boundary 136. The equivalent representation ofFIG. 8B can be modeled as an equivalent transmission line, as shown inFIG. 8C. The cross-section of the equivalent structure is represented asa (z-directed) end-loaded transmission line, with the impedance of theperfectly conducting image plane being a short circuit (z_(s)=0). Thedepth z₁ can be determined by equating the TEM wave impedance lookingdown at the Earth to an image ground plane impedance z_(in) seen lookinginto the transmission line of FIG. 8C.

In the case of FIG. 8A, the propagation constant and wave intrinsicimpedance in the upper region (air) 142 are

$\begin{matrix}{{\gamma_{o} = {{j\; \omega \sqrt{\mu_{o}ɛ_{o}}} = {0 + {j\; \beta_{o}}}}},{and}} & (55) \\{z_{o} = {\frac{j\; {\omega\mu}_{o}}{\gamma_{o}} = {\sqrt{\frac{\mu_{o}}{ɛ_{o}}}.}}} & (56)\end{matrix}$

In the lossy Earth 133, the propagation constant and wave intrinsicimpedance are

$\begin{matrix}{{\gamma_{e} = \sqrt{j\; {{\omega\mu}_{1}( {\sigma_{1} + {j\; {\omega ɛ}_{1}}} )}}},{and}} & (57) \\{Z_{e} = {\frac{j\; {\omega\mu}_{1}}{\gamma_{e}}.}} & (58)\end{matrix}$

For normal incidence, the equivalent representation of FIG. 8B isequivalent to a TEM transmission line whose characteristic impedance isthat of air (z₀), with propagation constant of γ₀, and whose length isz₁. As such, the image ground plane impedance Z_(in) seen at theinterface for the shorted transmission line of FIG. 8C is given by

Z _(in) =Z ₀ tan h(γ₀ z ₁).  (59)

Equating the image ground plane impedance Z_(in) associated with theequivalent model of FIG. 8C to the normal incidence wave impedance ofFIG. 8A and solving for z₁ gives the distance to a short circuit (theperfectly conducting image ground plane 139)

$\begin{matrix}{{z_{1} = {{\frac{1}{\gamma_{o}}{\tanh^{- 1}( \frac{Z_{e}}{Z_{o}} )}} = {{\frac{1}{\gamma_{o}}{\tanh^{- 1}( \frac{\gamma_{o}}{\gamma_{e}} )}} \approx \frac{1}{\gamma_{e}}}}},} & (60)\end{matrix}$

where only the first term of the series expansion for the inversehyperbolic tangent is considered for this approximation. Note that inthe air region 142, the propagation constant is γ₀=Jβ₀, so Z_(in)=jZ₀tan β₀z₁ (which is a purely imaginary quantity for a real z₁), but z_(e)is a complex value if a σ≠0. Therefore, Z_(in)=Z_(e) only when z₁ is acomplex distance.

Since the equivalent representation of FIG. 8B includes a perfectlyconducting image ground plane 139, the image depth for a charge orcurrent lying at the surface of the Earth (physical boundary 136) isequal to distance z₁ on the other side of the image ground plane 139, ord=2×z₁ beneath the Earth's surface (which is located at z=0). Thus, thedistance to the perfectly conducting image ground plane 139 can beapproximated by

$\begin{matrix}{d = {{2z_{1}} \approx {\frac{2}{\gamma_{e}}.}}} & (61)\end{matrix}$

Additionally, the “image charge” will be “equal and opposite” to thereal charge, so the potential of the perfectly conducting image groundplane 139 at depth z₁=−d/2 will be zero.

If a charge Q₁ is elevated a distance H₁ above the surface of the Earthas illustrated in FIG. 3, then the image charge Q₁′ resides at a complexdistance of D₁=d+H₁ below the surface, or a complex distance of d/2+H₁below the image ground plane 130. The guided surface waveguide probe 200b of FIG. 7 can be modeled as an equivalent single-wire transmissionline image plane model that can be based upon the perfectly conductingimage ground plane 139 of FIG. 8B. FIG. 9A shows an example of theequivalent single-wire transmission line image plane model, and FIG. 9Billustrates an example of the equivalent classic transmission linemodel, including the shorted transmission line of FIG. 8C.

In the equivalent image plane models of FIGS. 9A and 9B, Φ=θ_(y)+θ_(c)is the traveling wave phase delay of the guided surface waveguide probe200 referenced to Earth 133 (or the lossy conducting medium 203),θ_(c)=β_(p)H is the electrical length of the coil 215 (FIG. 7), ofphysical length H, expressed in degrees, θ_(y)=β_(w)h_(w) is theelectrical length of the vertical feed line conductor 221 (FIG. 7), ofphysical length h_(w), expressed in degrees, and θ_(d)=β₀ d/2 is thephase shift between the image ground plane 139 and the physical boundary136 of the Earth 133 (or lossy conducting medium 203). In the example ofFIGS. 9A and 9B, Z_(w) is the characteristic impedance of the elevatedvertical feed line conductor 221 in ohms, Z_(c) is the characteristicimpedance of the coil 215 in ohms, and Z_(O) is the characteristicimpedance of free space.

At the base of the guided surface waveguide probe 200, the impedanceseen “looking up” into the structure is Z_(⬆)=Z_(base). With a loadimpedance of:

$\begin{matrix}{{Z_{L} = \frac{1}{j\; \omega \; C_{T}}},} & (62)\end{matrix}$

where C_(T) is the self-capacitance of the charge terminal T₁, theimpedance seen “looking up” into the vertical feed line conductor 221(FIG. 7) is given by:

$\begin{matrix}{{Z_{2} = {{Z_{W}\frac{Z_{L} + {Z_{w}{\tanh ( {j\; \beta_{w}h_{w}} )}}}{Z_{w} + {Z_{L}{\tanh ( {j\; \beta_{w}h_{w}} )}}}} = {Z_{W}\frac{Z_{L} + {Z_{w}{\tanh ( {j\; \theta_{y}} )}}}{Z_{w} + {Z_{L}{\tanh ( {j\; \theta_{y}} )}}}}}},} & (63)\end{matrix}$

and the impedance seen “looking up” into the coil 215 (FIG. 7) is givenby:

$\begin{matrix}{Z_{base} = {{Z_{c}\frac{Z_{2} + {Z_{c}{\tanh ( {j\; \beta_{p}H} )}}}{Z_{c} + {Z_{2}{\tanh ( {j\; \beta_{p}H} )}}}} = {Z_{c}{\frac{Z_{2} + {Z_{c}{\tanh ( {j\; \theta_{c}} )}}}{Z_{c} + {Z_{2}{\tanh ( {j\; \theta_{c}} )}}}.}}}} & (64)\end{matrix}$

At the base of the guided surface waveguide probe 200, the impedanceseen “looking down” into the lossy conducting medium 203 isZ_(⬇)=Z_(in), which is given by:

$\begin{matrix}{{Z_{in} = {{Z_{o}\frac{Z_{s} + {Z_{o}{\tanh \lbrack {j\; {\beta_{o}( {d/2} )}} \rbrack}}}{Z_{o} + {Z_{s}{\tanh \lbrack {j\; {\beta_{o}( {d/2} )}} \rbrack}}}} = {Z_{o}{\tanh ( {j\; \theta_{d}} )}}}},} & (65)\end{matrix}$

where Z_(s)=0.

Neglecting losses, the equivalent image plane model can be tuned toresonance when Z_(⬇)+Z_(⬆)=0 at the physical boundary 136. Or, in thelow loss case, X_(⬇)+X_(⬆)=0 at the physical boundary 136, where X isthe corresponding reactive component. Thus, the impedance at thephysical boundary 136 “looking up” into the guided surface waveguideprobe 200 is the conjugate of the impedance at the physical boundary 136“looking down” into the lossy conducting medium 203. By adjusting theload impedance Z_(L) of the charge terminal T₁ while maintaining thetraveling wave phase delay Φ equal to the angle of the media's wave tiltΨ, so that Φ=Ψ, which improves and/or maximizes coupling of the probe'selectric field to a guided surface waveguide mode along the surface ofthe lossy conducting medium 203 (e.g., Earth), the equivalent imageplane models of FIGS. 9A and 9B can be tuned to resonance with respectto the image ground plane 139. In this way, the impedance of theequivalent complex image plane model is purely resistive, whichmaintains a superposed standing wave on the probe structure thatmaximizes the voltage and elevated charge on terminal T₁, and byequations (1)-(3) and (16) maximizes the propagating surface wave.

It follows from the Hankel solutions, that the guided surface waveexcited by the guided surface waveguide probe 200 is an outwardpropagating traveling wave. The source distribution along the feednetwork 209 between the charge terminal T₁ and the ground stake 218 ofthe guided surface waveguide probe 200 (FIGS. 3 and 7) is actuallycomposed of a superposition of a traveling wave plus a standing wave onthe structure. With the charge terminal T₁ positioned at or above thephysical height h_(p), the phase delay of the traveling wave movingthrough the feed network 209 is matched to the angle of the wave tiltassociated with the lossy conducting medium 203. This mode-matchingallows the traveling wave to be launched along the lossy conductingmedium 203. Once the phase delay has been established for the travelingwave, the load impedance Z_(L) of the charge terminal T₁ is adjusted tobring the probe structure into standing wave resonance with respect tothe image ground plane (130 of FIG. 3 or 139 of FIG. 8), which is at acomplex depth of −d/2. In that case, the impedance seen from the imageground plane has zero reactance and the charge on the charge terminal T₁is maximized.

The distinction between the traveling wave phenomenon and standing wavephenomena is that (1) the phase delay of traveling waves (θ=β_(d)) on asection of transmission line of length d (sometimes called a “delayline”) is due to propagation time delays; whereas (2) theposition-dependent phase of standing waves (which are composed offorward and backward propagating waves) depends on both the line lengthpropagation time delay and impedance transitions at interfaces betweenline sections of different characteristic impedances. In addition to thephase delay that arises due to the physical length of a section oftransmission line operating in sinusoidal steady-state, there is anextra reflection coefficient phase at impedance discontinuities that isdue to the ratio of Z_(oa)/Z_(ob), where Z_(oa) and Z_(ob) are thecharacteristic impedances of two sections of a transmission line suchas, e.g., a helical coil section of characteristic impedanceZ_(oa)=Z_(c) (FIG. 9B) and a straight section of vertical feed lineconductor of characteristic impedance Z_(ob)=Z_(w) (FIG. 9B).

As a result of this phenomenon, two relatively short transmission linesections of widely differing characteristic impedance may be used toprovide a very large phase shift. For example, a probe structurecomposed of two sections of transmission line, one of low impedance andone of high impedance, together totaling a physical length of, say,0.05λ, may be fabricated to provide a phase shift of 90° which isequivalent to a 0.25λ resonance. This is due to the large jump incharacteristic impedances. In this way, a physically short probestructure can be electrically longer than the two physical lengthscombined. This is illustrated in FIGS. 9A and 9B, where thediscontinuities in the impedance ratios provide large jumps in phase.The impedance discontinuity provides a substantial phase shift where thesections are joined together.

Referring to FIG. 10, shown is a flow chart 150 illustrating an exampleof adjusting a guided surface waveguide probe 200 (FIGS. 3 and 7) tosubstantially mode-match to a guided surface waveguide mode on thesurface of the lossy conducting medium, which launches a guided surfacetraveling wave along the surface of a lossy conducting medium 203 (FIG.3). Beginning with 153, the charge terminal T₁ of the guided surfacewaveguide probe 200 is positioned at a defined height above a lossyconducting medium 203. Utilizing the characteristics of the lossyconducting medium 203 and the operating frequency of the guided surfacewaveguide probe 200, the Hankel crossover distance can also be found byequating the magnitudes of Equations (20b) and (21) for −jγρ, andsolving for R_(x) as illustrated by FIG. 4. The complex index ofrefraction (n) can be determined using Equation (41), and the complexBrewster angle (θ_(i,B)) can then be determined from Equation (42). Thephysical height (h_(p)) of the charge terminal T₁ can then be determinedfrom Equation (44). The charge terminal T₁ should be at or higher thanthe physical height (h_(p)) in order to excite the far-out component ofthe Hankel function. This height relationship is initially consideredwhen launching surface waves. To reduce or minimize the bound charge onthe charge terminal T₁, the height should be at least four times thespherical diameter (or equivalent spherical diameter) of the chargeterminal T₁.

At 156, the electrical phase delay Φ of the elevated charge Q₁ on thecharge terminal T₁ is matched to the complex wave tilt angle Ψ. Thephase delay (θ_(c)) of the helical coil and/or the phase delay (θ_(y))of the vertical feed line conductor can be adjusted to make Φ equal tothe angle (Ψ) of the wave tilt (W). Based on Equation (31), the angle(Ψ) of the wave tilt can be determined from:

$\begin{matrix}{W = {\frac{E_{\rho}}{E_{z}} = {\frac{1}{\tan \; \theta_{i,B}} = {\frac{1}{n} = {{W}{e^{\; {j\; \Psi}}.}}}}}} & (66)\end{matrix}$

The electrical phase D can then be matched to the angle of the wavetilt. This angular (or phase) relationship is next considered whenlaunching surface waves. For example, the electrical phase delayΦ=θ_(c)+θ_(y) can be adjusted by varying the geometrical parameters ofthe coil 215 (FIG. 7) and/or the length (or height) of the vertical feedline conductor 221 (FIG. 7). By matching Φ=Ψ, an electric field can beestablished at or beyond the Hankel crossover distance (R_(x)) with acomplex Brewster angle at the boundary interface to excite the surfacewaveguide mode and launch a traveling wave along the lossy conductingmedium 203.

Next at 159, the load impedance of the charge terminal T₁ is tuned toresonate the equivalent image plane model of the guided surfacewaveguide probe 200. The depth (d/2) of the conducting image groundplane 139 of FIGS. 9A and 9B (or 130 of FIG. 3) can be determined usingEquations (52), (53) and (54) and the values of the lossy conductingmedium 203 (e.g., the Earth), which can be measured. Using that depth,the phase shift (θ_(d)) between the image ground plane 139 and thephysical boundary 136 of the lossy conducting medium 203 can bedetermined using θ_(d)=β_(o) d/2. The impedance (Z_(in)) as seen“looking down” into the lossy conducting medium 203 can then bedetermined using Equation (65). This resonance relationship can beconsidered to maximize the launched surface waves.

Based upon the adjusted parameters of the coil 215 and the length of thevertical feed line conductor 221, the velocity factor, phase delay, andimpedance of the coil 215 and vertical feed line conductor 221 can bedetermined using Equations (45) through (51). In addition, theself-capacitance (C_(T)) of the charge terminal T₁ can be determinedusing, e.g., Equation (24). The propagation factor (β_(p)) of the coil215 can be determined using Equation (35) and the propagation phaseconstant (β_(w)) for the vertical feed line conductor 221 can bedetermined using Equation (49). Using the self-capacitance and thedetermined values of the coil 215 and vertical feed line conductor 221,the impedance (Z_(base)) of the guided surface waveguide probe 200 asseen “looking up” into the coil 215 can be determined using Equations(62), (63) and (64).

The equivalent image plane model of the guided surface waveguide probe200 can be tuned to resonance by adjusting the load impedance Z_(L) suchthat the reactance component X_(base) Of Z_(base) cancels out thereactance component X_(in) of Z_(in), or X_(base)+X_(in)=0. Thus, theimpedance at the physical boundary 136 “looking up” into the guidedsurface waveguide probe 200 is the conjugate of the impedance at thephysical boundary 136 “looking down” into the lossy conducting medium203. The load impedance Z_(L) can be adjusted by varying the capacitance(C_(T)) of the charge terminal T₁ without changing the electrical phasedelay Φ=θ_(c)+θ_(y) of the charge terminal T₁. An iterative approach maybe taken to tune the load impedance Z_(L) for resonance of theequivalent image plane model with respect to the conducting image groundplane 139 (or 130). In this way, the coupling of the electric field to aguided surface waveguide mode along the surface of the lossy conductingmedium 203 (e.g., Earth) can be improved and/or maximized.

This may be better understood by illustrating the situation with anumerical example. Consider a guided surface waveguide probe 200comprising a top-loaded vertical stub of physical height h_(p) with acharge terminal T₁ at the top, where the charge terminal T₁ is excitedthrough a helical coil and vertical feed line conductor at anoperational frequency (f_(o)) of 1.85 MHz. With a height (H₁) of 16 feetand the lossy conducting medium 203 (e.g., Earth) having a relativepermittivity of ε_(r)=15 and a conductivity of σ₁=0.010 mhos/m, severalsurface wave propagation parameters can be calculated for f_(o)=1.850MHz. Under these conditions, the Hankel crossover distance can be foundto be R_(x)=54.5 feet with a physical height of h_(p)=5.5 feet, which iswell below the actual height of the charge terminal T₁. While a chargeterminal height of H₁=5.5 feet could have been used, the taller probestructure reduced the bound capacitance, permitting a greater percentageof free charge on the charge terminal T₁ providing greater fieldstrength and excitation of the traveling wave.

The wave length can be determined as:

$\begin{matrix}{{\lambda_{o} = {\frac{c}{f_{o}} = {162.162\mspace{14mu} {meters}}}},} & (67)\end{matrix}$

where c is the speed of light. The complex index of refraction is:

n=ε _(r) −jx=7.529−j6.546,  (68)

from Equation (41), where x=σ₁/ωε₀ with ω=2πf_(o), and the complexBrewster angle is:

θ_(i,B)=arctan(ε_(r) −jx)=85.6−j3.744°.  (69)

from Equation (42). Using Equation (66), the wave tilt values can bedetermined to be:

$\begin{matrix}{W = {\frac{1}{\tan \; \theta_{i,B}} = {\frac{1}{n} = {{{W}e^{\; {j\; \Psi}}} = {0.101{e^{j\; 40.614{^\circ}}.}}}}}} & (70)\end{matrix}$

Thus, the helical coil can be adjusted to match Φ=Ψ=40.614°

The velocity factor of the vertical feed line conductor (approximated asa uniform cylindrical conductor with a diameter of 0.27 inches) can begiven as V_(w)≈0.93. Since h_(p)<<λ₀, the propagation phase constant forthe vertical feed line conductor can be approximated as:

$\begin{matrix}{\beta_{w} = {\frac{2\pi}{\lambda_{w}} = {\frac{2\pi}{V_{w}\lambda_{0}} = {0.042\mspace{14mu} {m^{- 1}.}}}}} & (71)\end{matrix}$

From Equation (49) the phase delay of the vertical feed line conductoris:

θ_(y)=β_(w) h _(w)≈β_(w) h _(p)=11.640°.  (72)

By adjusting the phase delay of the helical coil so thatθ_(c)=28.974°=40.614°−11.640°, Φ will equal Ψ to match the guidedsurface waveguide mode. To illustrate the relationship between Φ and Ψ,FIG. 11 shows a plot of both over a range of frequencies. As both Φ andΨ are frequency dependent, it can be seen that their respective curvescross over each other at approximately 1.85 MHz.

For a helical coil having a conductor diameter of 0.0881 inches, a coildiameter (D) of 30 inches and a turn-to-turn spacing (s) of 4 inches,the velocity factor for the coil can be determined using Equation (45)as:

$\begin{matrix}{{V_{f} = {\frac{1}{\sqrt{1 + {20( \frac{D}{s} )^{2.5}( \frac{D}{\lambda_{o}} )^{0.5}}}} = 0.069}},} & (73)\end{matrix}$

and the propagation factor from Equation (35) is:

$\begin{matrix}{\beta_{p} = {\frac{2\pi}{V_{f}\lambda_{0}} = {0.564\mspace{14mu} {m^{- 1}.}}}} & (74)\end{matrix}$

With θ_(c)=28.9740, the axial length of the solenoidal helix (H) can bedetermined using Equation (46) such that:

$\begin{matrix}{H = {\frac{\theta_{c}}{\beta_{p}} = {35.2732\mspace{14mu} {{inches}.}}}} & (75)\end{matrix}$

This height determines the location on the helical coil where thevertical feed line conductor is connected, resulting in a coil with8.818 turns (N=H/s).

With the traveling wave phase delay of the coil and vertical feed lineconductor adjusted to match the wave tilt angle (Φ=θ_(c)+θ_(y)=Ψ), theload impedance (Z_(L)) of the charge terminal T₁ can be adjusted forstanding wave resonance of the equivalent image plane model of theguided surface wave probe 200. From the measured permittivity,conductivity and permeability of the Earth, the radial propagationconstant can be determined using Equation (57)

γ_(e)=√{square root over (jωu ₁(σ₁ +jωε ₁))}=0.25+j0.292m ⁻¹,  (76)

And the complex depth of the conducting image ground plane can beapproximated from Equation (52) as:

$\begin{matrix}{{{d \approx \frac{2}{\gamma_{e}}} = {3.364 + {j\; 3.963\mspace{14mu} {meters}}}},} & (77)\end{matrix}$

with a corresponding phase shift between the conducting image groundplane and the physical boundary of the Earth given by:

θ_(d)=β₀(d/2)=4.015−j4.73°.  (78)

Using Equation (65), the impedance seen “looking down” into the lossyconducting medium 203 (i.e., Earth) can be determined as:

Z _(in) =Z ₀ tan h(jθ _(d))=R _(in) +jX _(in)=31.191+j26.27 ohms.  (79)

By matching the reactive component (X_(in)) seen “looking down” into thelossy conducting medium 203 with the reactive component (X_(base)) seen“looking up” into the guided surface wave probe 200, the coupling intothe guided surface waveguide mode may be maximized. This can beaccomplished by adjusting the capacitance of the charge terminal T₁without changing the traveling wave phase delays of the coil andvertical feed line conductor. For example, by adjusting the chargeterminal capacitance (C_(T)) to 61.8126 pF, the load impedance fromEquation (62) is:

$\begin{matrix}{{Z_{L} = {\frac{1}{j\; \omega \; C_{T}} = {{- j}\mspace{11mu} 1392\mspace{14mu} {ohms}}}},} & (80)\end{matrix}$

and the reactive components at the boundary are matched.

Using Equation (51), the impedance of the vertical feed line conductor(having a diameter (2a) of 0.27 inches) is given as

$\begin{matrix}{{Z_{w} = {{138\; {\log ( \frac{1.123V_{w}\lambda_{0}}{2\; \pi \; a} )}} = {537.534\mspace{14mu} {ohms}}}},} & (81)\end{matrix}$

and the impedance seen “looking up” into the vertical feed lineconductor is given by Equation (63) as:

$\begin{matrix}{Z_{2} = {{Z_{W}\frac{Z_{L} + {Z_{w}\tan \; {h( {j\; \theta_{y}} )}}}{Z_{w} + {Z_{L}\tan \; {h( {j\; \theta_{y}} )}}}} = {{- j}\mspace{14mu} 835.438\mspace{14mu} {{ohms}.}}}} & (82)\end{matrix}$

Using Equation (47), the characteristic impedance of the helical coil isgiven as

$\begin{matrix}{{Z_{c} = {{\frac{60}{V_{f}}\lbrack {{\; {n( \frac{V_{f}\lambda_{0}}{D} )}} - 1.027} \rbrack} = {1446\mspace{14mu} {ohms}}}},} & (83)\end{matrix}$

and the impedance seen “looking up” into the coil at the base is givenby Equation (64) as:

$\begin{matrix}{Z_{base} = {{Z_{c}\frac{Z_{2} + {Z_{c}\tan \; {h( {j\; \theta_{c}} )}}}{Z_{c} + {Z_{2}\tan \; {h( {j\; \theta_{c}} )}}}} = {{- j}\mspace{14mu} 26.271\mspace{14mu} {{ohms}.}}}} & (84)\end{matrix}$

When compared to the solution of Equation (79), it can be seen that thereactive components are opposite and approximately equal, and thus areconjugates of each other. Thus, the impedance (Z_(ip)) seen “looking up”into the equivalent image plane model of FIGS. 9A and 9B from theperfectly conducting image ground plane is only resistive orZ_(ip)=R+j0.

When the electric fields produced by a guided surface waveguide probe200 (FIG. 3) are established by matching the traveling wave phase delayof the feed network to the wave tilt angle and the probe structure isresonated with respect to the perfectly conducting image ground plane atcomplex depth z=−d/2, the fields are substantially mode-matched to aguided surface waveguide mode on the surface of the lossy conductingmedium, a guided surface traveling wave is launched along the surface ofthe lossy conducting medium. As illustrated in FIG. 1, the guided fieldstrength curve 103 of the guided electromagnetic field has acharacteristic exponential decay of e^(−αd)/√{square root over (d)} andexhibits a distinctive knee 109 on the log-log scale.

In summary, both analytically and experimentally, the traveling wavecomponent on the structure of the guided surface waveguide probe 200 hasa phase delay (Φ) at its upper terminal that matches the angle (Ψ) ofthe wave tilt of the surface traveling wave (Φ=Ψ). Under this condition,the surface waveguide may be considered to be “mode-matched”.Furthermore, the resonant standing wave component on the structure ofthe guided surface waveguide probe 200 has a V_(MAX) at the chargeterminal T₁ and a V_(MIN) down at the image plane 139 (FIG. 8B) whereZ_(ip)=R_(ip)+j0 at a complex depth of z=−d/2, not at the connection atthe physical boundary 136 of the lossy conducting medium 203 (FIG. 8B).Lastly, the charge terminal T₁ is of sufficient height H₁ of FIG. 3(h≥R_(x) tan ψ_(i,B)) so that electromagnetic waves incident onto thelossy conducting medium 203 at the complex Brewster angle do so out at adistance (≥R_(x)) where the 1/√{square root over (r)} term ispredominant. Receive circuits can be utilized with one or more guidedsurface waveguide probes to facilitate wireless transmission and/orpower delivery systems.

Referring back to FIG. 3, operation of a guided surface waveguide probe200 may be controlled to adjust for variations in operational conditionsassociated with the guided surface waveguide probe 200. For example, anadaptive probe control system 230 can be used to control the feednetwork 209 and/or the charge terminal T₁ to control the operation ofthe guided surface waveguide probe 200. Operational conditions caninclude, but are not limited to, variations in the characteristics ofthe lossy conducting medium 203 (e.g., conductivity u and relativepermittivity ε_(r)), variations in field strength and/or variations inloading of the guided surface waveguide probe 200. As can be seen fromEquations (31), (41) and (42), the index of refraction (n), the complexBrewster angle (θ_(i,B)), and the wave tilt (|W|e^(jΨ)) can be affectedby changes in soil conductivity and permittivity resulting from, e.g.,weather conditions.

Equipment such as, e.g., conductivity measurement probes, permittivitysensors, ground parameter meters, field meters, current monitors and/orload receivers can be used to monitor for changes in the operationalconditions and provide information about current operational conditionsto the adaptive probe control system 230. The probe control system 230can then make one or more adjustments to the guided surface waveguideprobe 200 to maintain specified operational conditions for the guidedsurface waveguide probe 200. For instance, as the moisture andtemperature vary, the conductivity of the soil will also vary.Conductivity measurement probes and/or permittivity sensors may belocated at multiple locations around the guided surface waveguide probe200. Generally, it would be desirable to monitor the conductivity and/orpermittivity at or about the Hankel crossover distance R_(x) for theoperational frequency. Conductivity measurement probes and/orpermittivity sensors may be located at multiple locations (e.g., in eachquadrant) around the guided surface waveguide probe 200.

The conductivity measurement probes and/or permittivity sensors can beconfigured to evaluate the conductivity and/or permittivity on aperiodic basis and communicate the information to the probe controlsystem 230. The information may be communicated to the probe controlsystem 230 through a network such as, but not limited to, a LAN, WLAN,cellular network, or other appropriate wired or wireless communicationnetwork. Based upon the monitored conductivity and/or permittivity, theprobe control system 230 may evaluate the variation in the index ofrefraction (n), the complex Brewster angle (θ_(i,B)), and/or the wavetilt (|W|e^(jΨ)) and adjust the guided surface waveguide probe 200 tomaintain the phase delay (Φ) of the feed network 209 equal to the wavetilt angle (Ψ) and/or maintain resonance of the equivalent image planemodel of the guided surface waveguide probe 200. This can beaccomplished by adjusting, e.g., θ_(y), θ_(c) and/or C_(T). Forinstance, the probe control system 230 can adjust the self-capacitanceof the charge terminal T₁ and/or the phase delay (θ_(y), θ_(c)) appliedto the charge terminal T₁ to maintain the electrical launchingefficiency of the guided surface wave at or near its maximum. Forexample, the self-capacitance of the charge terminal T₁ can be varied bychanging the size of the terminal. The charge distribution can also beimproved by increasing the size of the charge terminal T₁, which canreduce the chance of an electrical discharge from the charge terminalT₁. In other embodiments, the charge terminal T₁ can include a variableinductance that can be adjusted to change the load impedance Z_(L). Thephase applied to the charge terminal T₁ can be adjusted by varying thetap position on the coil 215 (FIG. 7), and/or by including a pluralityof predefined taps along the coil 215 and switching between thedifferent predefined tap locations to maximize the launching efficiency.

Field or field strength (FS) meters may also be distributed about theguided surface waveguide probe 200 to measure field strength of fieldsassociated with the guided surface wave. The field or FS meters can beconfigured to detect the field strength and/or changes in the fieldstrength (e.g., electric field strength) and communicate thatinformation to the probe control system 230. The information may becommunicated to the probe control system 230 through a network such as,but not limited to, a LAN, WLAN, cellular network, or other appropriatecommunication network. As the load and/or environmental conditionschange or vary during operation, the guided surface waveguide probe 200may be adjusted to maintain specified field strength(s) at the FS meterlocations to ensure appropriate power transmission to the receivers andthe loads they supply.

For example, the phase delay (Φ=θ_(y)+θ_(c)) applied to the chargeterminal T₁ can be adjusted to match the wave tilt angle (Ψ). Byadjusting one or both phase delays, the guided surface waveguide probe200 can be adjusted to ensure the wave tilt corresponds to the complexBrewster angle. This can be accomplished by adjusting a tap position onthe coil 215 (FIG. 7) to change the phase delay supplied to the chargeterminal T₁. The voltage level supplied to the charge terminal T₁ canalso be increased or decreased to adjust the electric field strength.This may be accomplished by adjusting the output voltage of theexcitation source 212 or by adjusting or reconfiguring the feed network209. For instance, the position of the tap 227 (FIG. 7) for the ACsource 212 can be adjusted to increase the voltage seen by the chargeterminal T₁. Maintaining field strength levels within predefined rangescan improve coupling by the receivers, reduce ground current losses, andavoid interference with transmissions from other guided surfacewaveguide probes 200.

The probe control system 230 can be implemented with hardware, firmware,software executed by hardware, or a combination thereof. For example,the probe control system 230 can include processing circuitry includinga processor and a memory, both of which can be coupled to a localinterface such as, for example, a data bus with an accompanyingcontrol/address bus as can be appreciated by those with ordinary skillin the art. A probe control application may be executed by the processorto adjust the operation of the guided surface waveguide probe 200 basedupon monitored conditions. The probe control system 230 can also includeone or more network interfaces for communicating with the variousmonitoring devices. Communications can be through a network such as, butnot limited to, a LAN, WLAN, cellular network, or other appropriatecommunication network. The probe control system 230 may comprise, forexample, a computer system such as a server, desktop computer, laptop,or other system with like capability.

Referring back to the example of FIG. 5A, the complex angle trigonometryis shown for the ray optic interpretation of the incident electric field(E) of the charge terminal T₁ with a complex Brewster angle (θ_(i,B)) atthe Hankel crossover distance (R_(x)). Recall that, for a lossyconducting medium, the Brewster angle is complex and specified byequation (38). Electrically, the geometric parameters are related by theelectrical effective height (h_(eff)) of the charge terminal T₁ byequation (39). Since both the physical height (h_(p)) and the Hankelcrossover distance (R_(x)) are real quantities, the angle of the desiredguided surface wave tilt at the Hankel crossover distance (W_(Rx)) isequal to the phase (Φ) of the complex effective height (h_(eff)). Withthe charge terminal T₁ positioned at the physical height h_(p) andexcited with a charge having the appropriate phase c, the resultingelectric field is incident with the lossy conducting medium boundaryinterface at the Hankel crossover distance R_(x), and at the Brewsterangle. Under these conditions, the guided surface waveguide mode can beexcited without reflection or substantially negligible reflection.

However, Equation (39) means that the physical height of the guidedsurface waveguide probe 200 can be relatively small. While this willexcite the guided surface waveguide mode, this can result in an undulylarge bound charge with little free charge. To compensate, the chargeterminal T₁ can be raised to an appropriate elevation to increase theamount of free charge. As one example rule of thumb, the charge terminalT₁ can be positioned at an elevation of about 4-5 times (or more) theeffective diameter of the charge terminal T₁. FIG. 6 illustrates theeffect of raising the charge terminal T₁ above the physical height(h_(p)) shown in FIG. 5A. The increased elevation causes the distance atwhich the wave tilt is incident with the lossy conductive medium to movebeyond the Hankel crossover point 121 (FIG. 5A). To improve coupling inthe guided surface waveguide mode, and thus provide for a greaterlaunching efficiency of the guided surface wave, a lower compensationterminal T₂ can be used to adjust the total effective height (h_(TE)) ofthe charge terminal T₁ such that the wave tilt at the Hankel crossoverdistance is at the Brewster angle.

Referring to FIG. 12, shown is an example of a guided surface waveguideprobe 200 c that includes an elevated charge terminal T₁ and a lowercompensation terminal T₂ that are arranged along a vertical axis z thatis normal to a plane presented by the lossy conducting medium 203. Inthis respect, the charge terminal T₁ is placed directly above thecompensation terminal T₂ although it is possible that some otherarrangement of two or more charge and/or compensation terminals T_(N)can be used. The guided surface waveguide probe 200 c is disposed abovea lossy conducting medium 203 according to an embodiment of the presentdisclosure. The lossy conducting medium 203 makes up Region 1 with asecond medium 206 that makes up Region 2 sharing a boundary interfacewith the lossy conducting medium 203.

The guided surface waveguide probe 200 c includes a feed network 209that couples an excitation source 212 to the charge terminal T₁ and thecompensation terminal T₂. According to various embodiments, charges Q₁and Q₂ can be imposed on the respective charge and compensationterminals T₁ and T₂, depending on the voltages applied to terminals T₁and T₂ at any given instant. I₁ is the conduction current feeding thecharge Q₁ on the charge terminal T₁ via the terminal lead, and I₂ is theconduction current feeding the charge Q₂ on the compensation terminal T₂via the terminal lead.

According to the embodiment of FIG. 12, the charge terminal T₁ ispositioned over the lossy conducting medium 203 at a physical height H₁,and the compensation terminal T₂ is positioned directly below T₁ alongthe vertical axis z at a physical height H₂, where H₂ is less than H₁.The height h of the transmission structure may be calculated as h=H₁−H₂.The charge terminal T₁ has an isolated (or self) capacitance C₁, and thecompensation terminal T₂ has an isolated (or self) capacitance C₂. Amutual capacitance C_(M) can also exist between the terminals T₁ and T₂depending on the distance therebetween. During operation, charges Q₁ andQ₂ are imposed on the charge terminal T₁ and the compensation terminalT₂, respectively, depending on the voltages applied to the chargeterminal T₁ and the compensation terminal T₂ at any given instant.

Referring next to FIG. 13, shown is a ray optics interpretation of theeffects produced by the elevated charge Q₁ on charge terminal T₁ andcompensation terminal T₂ of FIG. 12. With the charge terminal T₁elevated to a height where the ray intersects with the lossy conductivemedium at the Brewster angle at a distance greater than the Hankelcrossover point 121 as illustrated by line 163, the compensationterminal T₂ can be used to adjust h_(TE) by compensating for theincreased height. The effect of the compensation terminal T₂ is toreduce the electrical effective height of the guided surface waveguideprobe (or effectively raise the lossy medium interface) such that thewave tilt at the Hankel crossover distance is at the Brewster angle asillustrated by line 166.

The total effective height can be written as the superposition of anupper effective height (h_(UE)) associated with the charge terminal T₁and a lower effective height (h_(LE)) associated with the compensationterminal T₂ such that

h _(TE) =h _(UE) +h _(LE) =h _(p) e ^(j(βh) ^(p) ^(+Φ) ^(U) ⁾ +h _(d) e^(j(βh) ^(d) ^(+Φ) ^(L) ⁾ =R _(x) ×W,  (85)

where Φ_(U) is the phase delay applied to the upper charge terminal T₁,Φ_(L) is the phase delay applied to the lower compensation terminal T₂,β=2π/λ_(p) is the propagation factor from Equation (35), h_(p) is thephysical height of the charge terminal T₁ and h_(d) is the physicalheight of the compensation terminal T₂. If extra lead lengths are takeninto consideration, they can be accounted for by adding the chargeterminal lead length z to the physical height h_(p) of the chargeterminal T₁ and the compensation terminal lead length y to the physicalheight h_(d) of the compensation terminal T₂ as shown in

h _(TE)=(h _(p) +z)e ^(j(β(h) ^(p) ^(+z)+Φ) ^(U) ⁾+(h _(d) +y)e ^(j(β(h)^(d) ^(+y)+Φ) ^(L) ⁾ =R _(x) ×W.  (86)

The lower effective height can be used to adjust the total effectiveheight (h_(TE)) to equal the complex effective height (h_(eff)) of FIG.5A.

Equations (85) or (86) can be used to determine the physical height ofthe lower disk of the compensation terminal T₂ and the phase angles tofeed the terminals in order to obtain the desired wave tilt at theHankel crossover distance. For example, Equation (86) can be rewrittenas the phase shift applied to the charge terminal T₁ as a function ofthe compensation terminal height (h_(d)) to give

$\begin{matrix}{{\Phi_{U}( h_{d} )} = {{- {\beta ( {h_{p} + z} )}} - {j\mspace{14mu} {{\ln ( \frac{{R_{x} \times W} - {( {h_{d} + y} )e^{j{({{\beta \; h_{d}} + {\beta \; y} + \Phi_{L}})}}}}{( {h_{p} + z} )} )}.}}}} & (87)\end{matrix}$

To determine the positioning of the compensation terminal T₂, therelationships discussed above can be utilized. First, the totaleffective height (h_(TE)) is the superposition of the complex effectiveheight (h_(UE)) of the upper charge terminal T₁ and the complexeffective height (h_(LE)) of the lower compensation terminal T₂ asexpressed in Equation (86). Next, the tangent of the angle of incidencecan be expressed geometrically as

$\begin{matrix}{{{\tan \; \psi_{E}} = \frac{h_{TE}}{R_{x}}},} & (88)\end{matrix}$

which is equal to the definition of the wave tilt, W. Finally, given thedesired Hankel crossover distance R_(x), the h_(TE) can be adjusted tomake the wave tilt of the incident ray match the complex Brewster angleat the Hankel crossover point 121. This can be accomplished by adjustingh_(p), Φ_(U), and/or h_(d).

These concepts may be better understood when discussed in the context ofan example of a guided surface waveguide probe. Referring to FIG. 14,shown is a graphical representation of an example of a guided surfacewaveguide probe 200 d including an upper charge terminal T₁ (e.g., asphere at height h_(T)) and a lower compensation terminal T₂ (e.g., adisk at height h_(d)) that are positioned along a vertical axis z thatis substantially normal to the plane presented by the lossy conductingmedium 203. During operation, charges Q₁ and Q₂ are imposed on thecharge and compensation terminals T₁ and T₂, respectively, depending onthe voltages applied to the terminals T₁ and T₂ at any given instant.

An AC source 212 acts as the excitation source for the charge terminalT₁, which is coupled to the guided surface waveguide probe 200 d througha feed network 209 comprising a coil 215 such as, e.g., a helical coil.The AC source 212 can be connected across a lower portion of the coil215 through a tap 227, as shown in FIG. 14, or can be inductivelycoupled to the coil 215 by way of a primary coil. The coil 215 can becoupled to a ground stake 218 at a first end and the charge terminal T₁at a second end. In some implementations, the connection to the chargeterminal T₁ can be adjusted using a tap 224 at the second end of thecoil 215. The compensation terminal T₂ is positioned above andsubstantially parallel with the lossy conducting medium 203 (e.g., theground or Earth), and energized through a tap 233 coupled to the coil215. An ammeter 236 located between the coil 215 and ground stake 218can be used to provide an indication of the magnitude of the currentflow (I₀) at the base of the guided surface waveguide probe.Alternatively, a current clamp may be used around the conductor coupledto the ground stake 218 to obtain an indication of the magnitude of thecurrent flow (I₀).

In the example of FIG. 14, the coil 215 is coupled to a ground stake 218at a first end and the charge terminal T₁ at a second end via a verticalfeed line conductor 221. In some implementations, the connection to thecharge terminal T₁ can be adjusted using a tap 224 at the second end ofthe coil 215 as shown in FIG. 14. The coil 215 can be energized at anoperating frequency by the AC source 212 through a tap 227 at a lowerportion of the coil 215. In other implementations, the AC source 212 canbe inductively coupled to the coil 215 through a primary coil. Thecompensation terminal T₂ is energized through a tap 233 coupled to thecoil 215. An ammeter 236 located between the coil 215 and ground stake218 can be used to provide an indication of the magnitude of the currentflow at the base of the guided surface waveguide probe 200 d.Alternatively, a current clamp may be used around the conductor coupledto the ground stake 218 to obtain an indication of the magnitude of thecurrent flow. The compensation terminal T₂ is positioned above andsubstantially parallel with the lossy conducting medium 203 (e.g., theground).

In the example of FIG. 14, the connection to the charge terminal T₁located on the coil 215 above the connection point of tap 233 for thecompensation terminal T₂. Such an adjustment allows an increased voltage(and thus a higher charge Q₁) to be applied to the upper charge terminalT₁. In other embodiments, the connection points for the charge terminalT₁ and the compensation terminal T₂ can be reversed. It is possible toadjust the total effective height (h_(TE)) of the guided surfacewaveguide probe 200 d to excite an electric field having a guidedsurface wave tilt at the Hankel crossover distance R_(x). The Hankelcrossover distance can also be found by equating the magnitudes ofequations (20b) and (21) for −jγρ, and solving for R_(x) as illustratedby FIG. 4. The index of refraction (n), the complex Brewster angle(θ_(i,B) and ψ_(i,B)), the wave tilt (|W|e^(jΨ)) and the complexeffective height (h_(eff)=h_(p)e^(jΦ)) can be determined as describedwith respect to Equations (41)-(44) above.

With the selected charge terminal T₁ configuration, a spherical diameter(or the effective spherical diameter) can be determined. For example, ifthe charge terminal T₁ is not configured as a sphere, then the terminalconfiguration may be modeled as a spherical capacitance having aneffective spherical diameter. The size of the charge terminal T₁ can bechosen to provide a sufficiently large surface for the charge Q₁ imposedon the terminals. In general, it is desirable to make the chargeterminal T₁ as large as practical. The size of the charge terminal T₁should be large enough to avoid ionization of the surrounding air, whichcan result in electrical discharge or sparking around the chargeterminal. To reduce the amount of bound charge on the charge terminalT₁, the desired elevation to provide free charge on the charge terminalT₁ for launching a guided surface wave should be at least 4-5 times theeffective spherical diameter above the lossy conductive medium (e.g.,the Earth). The compensation terminal T₂ can be used to adjust the totaleffective height (h_(TE)) of the guided surface waveguide probe 200 d toexcite an electric field having a guided surface wave tilt at R_(x). Thecompensation terminal T₂ can be positioned below the charge terminal T₁at h_(d)=h_(T)−h_(p), where h_(T) is the total physical height of thecharge terminal T₁. With the position of the compensation terminal T₂fixed and the phase delay Φ_(U) applied to the upper charge terminal T₁,the phase delay Φ_(L) applied to the lower compensation terminal T₂ canbe determined using the relationships of Equation (86), such that:

$\begin{matrix}{{\Phi_{U}( h_{d} )} = {{- {\beta ( {h_{d} + y} )}} - {j\mspace{14mu} {{\ln ( \frac{{R_{x} \times W} - {( {h_{p} + z} )e^{j{({{\beta \; h_{p}} + {\beta z} + \Phi_{L}})}}}}{( {h_{d} + y} )} )}.}}}} & (89)\end{matrix}$

In alternative embodiments, the compensation terminal T₂ can bepositioned at a height h_(d) where Im{Φ_(L)}=0. This is graphicallyillustrated in FIG. 15A, which shows plots 172 and 175 of the imaginaryand real parts of Φ_(L), respectively. The compensation terminal T₂ ispositioned at a height h_(d) where Im{Φ_(U)}=0, as graphicallyillustrated in plot 172. At this fixed height, the coil phase Φ_(U) canbe determined from Re{Φ_(U)}, as graphically illustrated in plot 175.

With the AC source 212 coupled to the coil 215 (e.g., at the 50Ω pointto maximize coupling), the position of tap 233 may be adjusted forparallel resonance of the compensation terminal T₂ with at least aportion of the coil at the frequency of operation. FIG. 15B shows aschematic diagram of the general electrical hookup of FIG. 14 in whichV₁ is the voltage applied to the lower portion of the coil 215 from theAC source 212 through tap 227, V₂ is the voltage at tap 224 that issupplied to the upper charge terminal T₁, and V₃ is the voltage appliedto the lower compensation terminal T₂ through tap 233. The resistancesR_(P) and R_(d) represent the ground return resistances of the chargeterminal T₁ and compensation terminal T₂, respectively. The charge andcompensation terminals T₁ and T₂ may be configured as spheres,cylinders, toroids, rings, hoods, or any other combination of capacitivestructures. The size of the charge and compensation terminals T₁ and T₂can be chosen to provide a sufficiently large surface for the charges Q₁and Q₂ imposed on the terminals. In general, it is desirable to make thecharge terminal T₁ as large as practical. The size of the chargeterminal T₁ should be large enough to avoid ionization of thesurrounding air, which can result in electrical discharge or sparkingaround the charge terminal. The self-capacitance C_(p) and C_(d) of thecharge and compensation terminals T₁ and T₂ respectively, can bedetermined using, for example, equation (24).

As can be seen in FIG. 15B, a resonant circuit is formed by at least aportion of the inductance of the coil 215, the self-capacitance C_(d) ofthe compensation terminal T₂, and the ground return resistance R_(d)associated with the compensation terminal T₂. The parallel resonance canbe established by adjusting the voltage V₃ applied to the compensationterminal T₂ (e.g., by adjusting a tap 233 position on the coil 215) orby adjusting the height and/or size of the compensation terminal T₂ toadjust C_(d). The position of the coil tap 233 can be adjusted forparallel resonance, which will result in the ground current through theground stake 218 and through the ammeter 236 reaching a maximum point.After parallel resonance of the compensation terminal T₂ has beenestablished, the position of the tap 227 for the AC source 212 can beadjusted to the 500 point on the coil 215.

Voltage V₂ from the coil 215 can be applied to the charge terminal T₁,and the position of tap 224 can be adjusted such that the phase (Φ) ofthe total effective height (h_(TE)) approximately equals the angle ofthe guided surface wave tilt (W_(Rx)) at the Hankel crossover distance(R_(x)). The position of the coil tap 224 can be adjusted until thisoperating point is reached, which results in the ground current throughthe ammeter 236 increasing to a maximum. At this point, the resultantfields excited by the guided surface waveguide probe 200 d aresubstantially mode-matched to a guided surface waveguide mode on thesurface of the lossy conducting medium 203, resulting in the launchingof a guided surface wave along the surface of the lossy conductingmedium 203. This can be verified by measuring field strength along aradial extending from the guided surface waveguide probe 200.

Resonance of the circuit including the compensation terminal T₂ maychange with the attachment of the charge terminal T₁ and/or withadjustment of the voltage applied to the charge terminal T₁ through tap224. While adjusting the compensation terminal circuit for resonanceaids the subsequent adjustment of the charge terminal connection, it isnot necessary to establish the guided surface wave tilt (W_(Rx)) at theHankel crossover distance (R_(x)). The system may be further adjusted toimprove coupling by iteratively adjusting the position of the tap 227for the AC source 212 to be at the 50Ω point on the coil 215 andadjusting the position of tap 233 to maximize the ground current throughthe ammeter 236. Resonance of the circuit including the compensationterminal T₂ may drift as the positions of taps 227 and 233 are adjusted,or when other components are attached to the coil 215.

In other implementations, the voltage V₂ from the coil 215 can beapplied to the charge terminal T₁, and the position of tap 233 can beadjusted such that the phase (Φ) of the total effective height (h_(TE))approximately equals the angle (Ψ) of the guided surface wave tilt atR_(x). The position of the coil tap 224 can be adjusted until theoperating point is reached, resulting in the ground current through theammeter 236 substantially reaching a maximum. The resultant fields aresubstantially mode-matched to a guided surface waveguide mode on thesurface of the lossy conducting medium 203, and a guided surface wave islaunched along the surface of the lossy conducting medium 203. This canbe verified by measuring field strength along a radial extending fromthe guided surface waveguide probe 200. The system may be furtheradjusted to improve coupling by iteratively adjusting the position ofthe tap 227 for the AC source 212 to be at the 50Ω point on the coil 215and adjusting the position of tap 224 and/or 233 to maximize the groundcurrent through the ammeter 236.

Referring back to FIG. 12, operation of a guided surface waveguide probe200 may be controlled to adjust for variations in operational conditionsassociated with the guided surface waveguide probe 200. For example, aprobe control system 230 can be used to control the feed network 209and/or positioning of the charge terminal T₁ and/or compensationterminal T₂ to control the operation of the guided surface waveguideprobe 200. Operational conditions can include, but are not limited to,variations in the characteristics of the lossy conducting medium 203(e.g., conductivity σ and relative permittivity ε_(r)), variations infield strength and/or variations in loading of the guided surfacewaveguide probe 200. As can be seen from Equations (41)-(44), the indexof refraction (n), the complex Brewster angle (θ_(i,B) and ψ_(i,B)), thewave tilt (|W|e^(jΨ)) and the complex effective height(h_(eff)=h_(p)e^(jΦ)) can be affected by changes in soil conductivityand permittivity resulting from, e.g., weather conditions.

Equipment such as, e.g., conductivity measurement probes, permittivitysensors, ground parameter meters, field meters, current monitors and/orload receivers can be used to monitor for changes in the operationalconditions and provide information about current operational conditionsto the probe control system 230. The probe control system 230 can thenmake one or more adjustments to the guided surface waveguide probe 200to maintain specified operational conditions for the guided surfacewaveguide probe 200. For instance, as the moisture and temperature vary,the conductivity of the soil will also vary. Conductivity measurementprobes and/or permittivity sensors may be located at multiple locationsaround the guided surface waveguide probe 200. Generally, it would bedesirable to monitor the conductivity and/or permittivity at or aboutthe Hankel crossover distance R_(x) for the operational frequency.Conductivity measurement probes and/or permittivity sensors may belocated at multiple locations (e.g., in each quadrant) around the guidedsurface waveguide probe 200.

With reference then to FIG. 16, shown is an example of a guided surfacewaveguide probe 200 e that includes a charge terminal T₁ and a chargeterminal T₂ that are arranged along a vertical axis z. The guidedsurface waveguide probe 200 e is disposed above a lossy conductingmedium 203, which makes up Region 1. In addition, a second medium 206shares a boundary interface with the lossy conducting medium 203 andmakes up Region 2. The charge terminals T₁ and T₂ are positioned overthe lossy conducting medium 203. The charge terminal T, is positioned atheight H₁, and the charge terminal T₂ is positioned directly below T₁along the vertical axis z at height H₂, where H₂ is less than H₁. Theheight h of the transmission structure presented by the guided surfacewaveguide probe 200 e is h=H₁−H₂. The guided surface waveguide probe 200e includes a feed network 209 that couples an excitation source 212 tothe charge terminals T₁ and T₂.

The charge terminals T₁ and/or T₂ include a conductive mass that canhold an electrical charge, which may be sized to hold as much charge aspractically possible. The charge terminal T₁ has a self-capacitance C₁,and the charge terminal T₂ has a self-capacitance C₂, which can bedetermined using, for example, equation (24). By virtue of the placementof the charge terminal T₁ directly above the charge terminal T₂, amutual capacitance C_(M) is created between the charge terminals T₁ andT₂. Note that the charge terminals T₁ and T₂ need not be identical, buteach can have a separate size and shape, and can include differentconducting materials. Ultimately, the field strength of a guided surfacewave launched by a guided surface waveguide probe 200 e is directlyproportional to the quantity of charge on the terminal T₁. The charge Q₁is, in turn, proportional to the self-capacitance C₁ associated with thecharge terminal T₁ since Q₁=C₁V, where V is the voltage imposed on thecharge terminal T₁.

When properly adjusted to operate at a predefined operating frequency,the guided surface waveguide probe 200 e generates a guided surface wavealong the surface of the lossy conducting medium 203. The excitationsource 212 can generate electrical energy at the predefined frequencythat is applied to the guided surface waveguide probe 200 e to excitethe structure. When the electromagnetic fields generated by the guidedsurface waveguide probe 200 e are substantially mode-matched with thelossy conducting medium 203, the electromagnetic fields substantiallysynthesize a wave front incident at a complex Brewster angle thatresults in little or no reflection. Thus, the surface waveguide probe200 e does not produce a radiated wave, but launches a guided surfacetraveling wave along the surface of a lossy conducting medium 203. Theenergy from the excitation source 212 can be transmitted as Zennecksurface currents to one or more receivers that are located within aneffective transmission range of the guided surface waveguide probe 200e.

One can determine asymptotes of the radial Zenneck surface currentJ_(ρ)(ρ) on the surface of the lossy conducting medium 203 to be J₁(ρ)close-in and J₂(ρ) far-out, where

$\begin{matrix}{{{{Close}\text{-}{in}\mspace{14mu} ( {\rho < {\lambda/8}} )\text{:}\mspace{14mu} {J_{\rho}(\rho)}\text{∼}J_{1}} = {\frac{I_{1} + I_{2}}{2\; \pi \; \rho} + \frac{{E_{\rho}^{QS}( Q_{1} )} + {E_{\rho}^{QS}( Q_{2} )}}{Z_{\rho}}}},{and}} & (90) \\{{{Far}\text{-}{out}\mspace{14mu} ( {\rho {\lambda/8}} )\text{:}\mspace{14mu} {J_{\rho}(\rho)}\text{∼}J_{2}} = {\frac{j\; \gamma \; \omega \; Q_{1}}{4} \times \sqrt{\frac{2\; \gamma}{\pi}} \times {\frac{e^{{- {({\alpha + {j\; \beta}})}}\rho}}{\sqrt{\rho}}.}}} & (91)\end{matrix}$

where I₁ is the conduction current feeding the charge Q₁ on the firstcharge terminal T₁, and I₂ is the conduction current feeding the chargeQ₂ on the second charge terminal T₂. The charge Q₁ on the upper chargeterminal T₁ is determined by Q₁=C₁V₁, where C₁ is the isolatedcapacitance of the charge terminal T₁. Note that there is a thirdcomponent to J₁ set forth above given by (E_(ρ) ^(Q) ¹ )/Z_(ρ), whichfollows from the Leontovich boundary condition and is the radial currentcontribution in the lossy conducting medium 203 pumped by thequasi-static field of the elevated oscillating charge on the firstcharge terminal Q₁. The quantity Z_(ρ)=jωμ_(o)/γ_(e) is the radialimpedance of the lossy conducting medium, whereγ_(e)=(jωμ₁σ₁−ω²μ₁ε₁)^(1/2).

The asymptotes representing the radial current close-in and far-out asset forth by equations (90) and (91) are complex quantities. Accordingto various embodiments, a physical surface current J(ρ), is synthesizedto match as close as possible the current asymptotes in magnitude andphase. That is to say close-in, |J(ρ)| is to be tangent to |J₁|, andfar-out |J(ρ)| is to be tangent to |J₂|. Also, according to the variousembodiments, the phase of J(ρ) should transition from the phase of J₁close-in to the phase of J₂ far-out.

In order to match the guided surface wave mode at the site oftransmission to launch a guided surface wave, the phase of the surfacecurrent |J₂| far-out should differ from the phase of the surface current|J₁| close-in by the propagation phase corresponding to e^(−jβ(ρ) ²^(-ρ) ¹ ⁾ plus a constant of approximately 45 degrees or 225 degrees.This is because there are two roots for √{square root over (γ)}, onenear π/4 and one near 5π/4. The properly adjusted synthetic radialsurface current is

$\begin{matrix}{{J_{\rho}( {\rho,\varphi,0} )} = {\frac{I_{0}\gamma}{4}{{H_{1}^{(2)}( {{- j}\; \gamma \; \rho} )}.}}} & (92)\end{matrix}$

Note that this is consistent with equation (17). By Maxwell's equations,such a J(ρ) surface current automatically creates fields that conform to

$\begin{matrix}{{H_{\varphi} = {\frac{{- \gamma}\; I_{o}}{4}e^{{- u_{2}}z}{H_{1}^{(2)}( {{- j}\; \gamma \; \rho} )}}},} & (93) \\{{E_{\rho} = {\frac{{- \gamma}\; I_{o}}{4}( \frac{u_{2}}{j\; \omega \; ɛ_{0}} )e^{{- u_{2}}z}{H_{1}^{(2)}( {{- j}\; \gamma \; \rho} )}}},{and}} & (94) \\{E_{z} = {\frac{{- \gamma}\; I_{o}}{4}( \frac{- \gamma}{\omega \; ɛ_{o}} )e^{{- u_{2}}z}{{H_{0}^{(2)}( {{- j}\; \gamma \; \rho} )}.}}} & (95)\end{matrix}$

Thus, the difference in phase between the surface current |J₂| far-outand the surface current |J₁| close-in for the guided surface wave modethat is to be matched is due to the characteristics of the Hankelfunctions in equations (93)-(95), which are consistent with equations(1)-(3). It is of significance to recognize that the fields expressed byequations (1)-(6) and (17) and equations (92)-(95) have the nature of atransmission line mode bound to a lossy interface, not radiation fieldsthat are associated with groundwave propagation.

In order to obtain the appropriate voltage magnitudes and phases for agiven design of a guided surface waveguide probe 200 e at a givenlocation, an iterative approach may be used. Specifically, analysis maybe performed of a given excitation and configuration of a guided surfacewaveguide probe 200 e taking into account the feed currents to theterminals T₁ and T₂, the charges on the charge terminals T₁ and T₂, andtheir images in the lossy conducting medium 203 in order to determinethe radial surface current density generated. This process may beperformed iteratively until an optimal configuration and excitation fora given guided surface waveguide probe 200 e is determined based ondesired parameters. To aid in determining whether a given guided surfacewaveguide probe 200 e is operating at an optimal level, a guided fieldstrength curve 103 (FIG. 1) may be generated using equations (1)-(12)based on values for the conductivity of Region 1 (σ₁) and thepermittivity of Region 1 (ε₁) at the location of the guided surfacewaveguide probe 200 e. Such a guided field strength curve 103 canprovide a benchmark for operation such that measured field strengths canbe compared with the magnitudes indicated by the guided field strengthcurve 103 to determine if optimal transmission has been achieved.

In order to arrive at an optimized condition, various parametersassociated with the guided surface waveguide probe 200 e may beadjusted. One parameter that may be varied to adjust the guided surfacewaveguide probe 200 e is the height of one or both of the chargeterminals T₁ and/or T₂ relative to the surface of the lossy conductingmedium 203. In addition, the distance or spacing between the chargeterminals T₁ and T₂ may also be adjusted. In doing so, one may minimizeor otherwise alter the mutual capacitance C_(M) or any boundcapacitances between the charge terminals T₁ and T₂ and the lossyconducting medium 203 as can be appreciated. The size of the respectivecharge terminals T₁ and/or T₂ can also be adjusted. By changing the sizeof the charge terminals T₁ and/or T₂, one will alter the respectiveself-capacitances C₁ and/or C₂, and the mutual capacitance C_(M) as canbe appreciated.

Still further, another parameter that can be adjusted is the feednetwork 209 associated with the guided surface waveguide probe 200 e.This may be accomplished by adjusting the size of the inductive and/orcapacitive reactances that make up the feed network 209. For example,where such inductive reactances comprise coils, the number of turns onsuch coils may be adjusted. Ultimately, the adjustments to the feednetwork 209 can be made to alter the electrical length of the feednetwork 209, thereby affecting the voltage magnitudes and phases on thecharge terminals T₁ and T₂.

Note that the iterations of transmission performed by making the variousadjustments may be implemented by using computer models or by adjustingphysical structures as can be appreciated. By making the aboveadjustments, one can create corresponding “close-in” surface current J₁and “far-out” surface current J₂ that approximate the same currents J(ρ)of the guided surface wave mode specified in Equations (90) and (91) setforth above. In doing so, the resulting electromagnetic fields would besubstantially or approximately mode-matched to a guided surface wavemode on the surface of the lossy conducting medium 203.

While not shown in the example of FIG. 16, operation of the guidedsurface waveguide probe 200 e may be controlled to adjust for variationsin operational conditions associated with the guided surface waveguideprobe 200. For example, a probe control system 230 shown in FIG. 12 canbe used to control the feed network 209 and/or positioning and/or sizeof the charge terminals T₁ and/or T₂ to control the operation of theguided surface waveguide probe 200 e. Operational conditions caninclude, but are not limited to, variations in the characteristics ofthe lossy conducting medium 203 (e.g., conductivity u and relativepermittivity ε_(r)), variations in field strength and/or variations inloading of the guided surface waveguide probe 200 e.

Referring now to FIG. 17, shown is an example of the guided surfacewaveguide probe 200 e of FIG. 16, denoted herein as guided surfacewaveguide probe 200 f. The guided surface waveguide probe 200 f includesthe charge terminals T₁ and T₂ that are positioned along a vertical axisz that is substantially normal to the plane presented by the lossyconducting medium 203 (e.g., the Earth). The second medium 206 is abovethe lossy conducting medium 203. The charge terminal T₁ has aself-capacitance C₁, and the charge terminal T₂ has a self-capacitanceC₂. During operation, charges Q₁ and Q₂ are imposed on the chargeterminals T₁ and T₂, respectively, depending on the voltages applied tothe charge terminals T₁ and T₂ at any given instant. A mutualcapacitance C_(M) may exist between the charge terminals T₁ and T₂depending on the distance there between. In addition, bound capacitancesmay exist between the respective charge terminals T₁ and T₂ and thelossy conducting medium 203 depending on the heights of the respectivecharge terminals T₁ and T₂ with respect to the lossy conducting medium203.

The guided surface waveguide probe 200 f includes a feed network 209that comprises an inductive impedance comprising a coil L_(1a) having apair of leads that are coupled to respective ones of the chargeterminals T₁ and T₂. In one embodiment, the coil L_(1a) is specified tohave an electrical length that is one-half (½) of the wavelength at theoperating frequency of the guided surface waveguide probe 200 f.

While the electrical length of the coil L_(1a) is specified asapproximately one-half (½) the wavelength at the operating frequency, itis understood that the coil L_(1a) may be specified with an electricallength at other values. According to one embodiment, the fact that thecoil L_(1a) has an electrical length of approximately one-half thewavelength at the operating frequency provides for an advantage in thata maximum voltage differential is created on the charge terminals T₁ andT₂. Nonetheless, the length or diameter of the coil L_(1a) may beincreased or decreased when adjusting the guided surface waveguide probe200 f to obtain optimal excitation of a guided surface wave mode.Adjustment of the coil length may be provided by taps located at one orboth ends of the coil. In other embodiments, it may be the case that theinductive impedance is specified to have an electrical length that issignificantly less than or greater than ½ the wavelength at theoperating frequency of the guided surface waveguide probe 200 f.

The excitation source 212 can be coupled to the feed network 209 by wayof magnetic coupling. Specifically, the excitation source 212 is coupledto a coil L_(P) that is inductively coupled to the coil L_(1a). This maybe done by link coupling, a tapped coil, a variable reactance, or othercoupling approach as can be appreciated. To this end, the coil L_(P)acts as a primary, and the coil L_(1a) acts as a secondary as can beappreciated.

In order to adjust the guided surface waveguide probe 200 f for thetransmission of a desired guided surface wave, the heights of therespective charge terminals T₁ and T₂ may be altered with respect to thelossy conducting medium 203 and with respect to each other. Also, thesizes of the charge terminals T₁ and T₂ may be altered. In addition, thesize of the coil L_(1a) may be altered by adding or eliminating turns orby changing some other dimension of the coil L_(1a). The coil L_(1a) canalso include one or more taps for adjusting the electrical length asshown in FIG. 17. The position of a tap connected to either chargeterminal T₁ or T₂ can also be adjusted.

Referring next to FIGS. 18A, 18B, 18C and 19, shown are examples ofgeneralized receive circuits for using the surface-guided waves inwireless power delivery systems. FIGS. 18A and 18B-18C include a linearprobe 303 and a tuned resonator 306, respectively. FIG. 19 is a magneticcoil 309 according to various embodiments of the present disclosure.According to various embodiments, each one of the linear probe 303, thetuned resonator 306, and the magnetic coil 309 may be employed toreceive power transmitted in the form of a guided surface wave on thesurface of a lossy conducting medium 203 according to variousembodiments. As mentioned above, in one embodiment the lossy conductingmedium 203 comprises a terrestrial medium (or Earth).

With specific reference to FIG. 18A, the open-circuit terminal voltageat the output terminals 312 of the linear probe 303 depends upon theeffective height of the linear probe 303. To this end, the terminalpoint voltage may be calculated as

V _(T)=∫₀ ^(h) ^(e) E _(inc) ·dl,  (96)

where E_(inc) is the strength of the incident electric field induced onthe linear probe 303 in Volts per meter, dl is an element of integrationalong the direction of the linear probe 303, and h_(e) is the effectiveheight of the linear probe 303. An electrical load 315 is coupled to theoutput terminals 312 through an impedance matching network 318.

When the linear probe 303 is subjected to a guided surface wave asdescribed above, a voltage is developed across the output terminals 312that may be applied to the electrical load 315 through a conjugateimpedance matching network 318 as the case may be. In order tofacilitate the flow of power to the electrical load 315, the electricalload 315 should be substantially impedance matched to the linear probe303 as will be described below.

Referring to FIG. 18B, a ground current excited coil 306 a possessing aphase shift equal to the wave tilt of the guided surface wave includes acharge terminal T_(R) that is elevated (or suspended) above the lossyconducting medium 203. The charge terminal T_(R) has a self-capacitanceC_(R). In addition, there may also be a bound capacitance (not shown)between the charge terminal T_(R) and the lossy conducting medium 203depending on the height of the charge terminal T_(R) above the lossyconducting medium 203. The bound capacitance should preferably beminimized as much as is practicable, although this may not be entirelynecessary in every instance.

The tuned resonator 306 a also includes a receiver network comprising acoil L_(R) having a phase shift Φ. One end of the coil L_(R) is coupledto the charge terminal T_(R), and the other end of the coil L_(R) iscoupled to the lossy conducting medium 203. The receiver network caninclude a vertical supply line conductor that couples the coil L_(R) tothe charge terminal T_(R). To this end, the coil L_(R) (which may alsobe referred to as tuned resonator L_(R)−C_(R)) comprises aseries-adjusted resonator as the charge terminal C_(R) and the coilL_(R) are situated in series. The phase delay of the coil L_(R) can beadjusted by changing the size and/or height of the charge terminalT_(R), and/or adjusting the size of the coil L_(R) so that the phase (ofthe structure is made substantially equal to the angle of the wave tiltΨ. The phase delay of the vertical supply line can also be adjusted by,e.g., changing length of the conductor.

For example, the reactance presented by the self-capacitance C_(R) iscalculated as 1/jωC_(R). Note that the total capacitance of thestructure 306 a may also include capacitance between the charge terminalT_(R) and the lossy conducting medium 203, where the total capacitanceof the structure 306 a may be calculated from both the self-capacitanceC_(R) and any bound capacitance as can be appreciated. According to oneembodiment, the charge terminal T_(R) may be raised to a height so as tosubstantially reduce or eliminate any bound capacitance. The existenceof a bound capacitance may be determined from capacitance measurementsbetween the charge terminal T_(R) and the lossy conducting medium 203 aspreviously discussed.

The inductive reactance presented by a discrete-element coil L_(R) maybe calculated as jωL, where L is the lumped-element inductance of thecoil L_(R). If the coil L_(R) is a distributed element, its equivalentterminal-point inductive reactance may be determined by conventionalapproaches. To tune the structure 306 a, one would make adjustments sothat the phase delay is equal to the wave tilt for the purpose ofmode-matching to the surface waveguide at the frequency of operation.Under this condition, the receiving structure may be considered to be“mode-matched” with the surface waveguide. A transformer link around thestructure and/or an impedance matching network 324 may be insertedbetween the probe and the electrical load 327 in order to couple powerto the load. Inserting the impedance matching network 324 between theprobe terminals 321 and the electrical load 327 can effect aconjugate-match condition for maximum power transfer to the electricalload 327.

When placed in the presence of surface currents at the operatingfrequencies power will be delivered from the surface guided wave to theelectrical load 327. To this end, an electrical load 327 may be coupledto the structure 306 a by way of magnetic coupling, capacitive coupling,or conductive (direct tap) coupling. The elements of the couplingnetwork may be lumped components or distributed elements as can beappreciated.

In the embodiment shown in FIG. 18B, magnetic coupling is employed wherea coil L_(S) is positioned as a secondary relative to the coil L_(R)that acts as a transformer primary. The coil L_(S) may be link-coupledto the coil L_(R) by geometrically winding it around the same corestructure and adjusting the coupled magnetic flux as can be appreciated.In addition, while the receiving structure 306 a comprises aseries-tuned resonator, a parallel-tuned resonator or even adistributed-element resonator of the appropriate phase delay may also beused.

While a receiving structure immersed in an electromagnetic field maycouple energy from the field, it can be appreciated thatpolarization-matched structures work best by maximizing the coupling,and conventional rules for probe-coupling to waveguide modes should beobserved. For example, a TE₂₀ (transverse electric mode) waveguide probemay be optimal for extracting energy from a conventional waveguideexcited in the TE₂₀ mode. Similarly, in these cases, a mode-matched andphase-matched receiving structure can be optimized for coupling powerfrom a surface-guided wave. The guided surface wave excited by a guidedsurface waveguide probe 200 on the surface of the lossy conductingmedium 203 can be considered a waveguide mode of an open waveguide.Excluding waveguide losses, the source energy can be completelyrecovered. Useful receiving structures may be E-field coupled, H-fieldcoupled, or surface-current excited.

The receiving structure can be adjusted to increase or maximize couplingwith the guided surface wave based upon the local characteristics of thelossy conducting medium 203 in the vicinity of the receiving structure.To accomplish this, the phase delay (Φ) of the receiving structure canbe adjusted to match the angle (Ψ) of the wave tilt of the surfacetraveling wave at the receiving structure. If configured appropriately,the receiving structure may then be tuned for resonance with respect tothe perfectly conducting image ground plane at complex depth z=−d/2.

For example, consider a receiving structure comprising the tunedresonator 306 a of FIG. 18B, including a coil L_(R) and a verticalsupply line connected between the coil L_(R) and a charge terminalT_(R). With the charge terminal T_(R) positioned at a defined heightabove the lossy conducting medium 203, the total phase shift C of thecoil L_(R) and vertical supply line can be matched with the angle (Ψ) ofthe wave tilt at the location of the tuned resonator 306 a. FromEquation (22), it can be seen that the wave tilt asymptotically passesto

$\begin{matrix}{{W = {{{W}e^{j\; \Psi}} = {\frac{E_{\rho}}{E_{z}}\underset{\rhoarrow\infty}{arrow}\frac{1}{\sqrt{ɛ_{r} - {j\frac{\sigma_{1}}{\omega \; ɛ_{o}}}}}}}},} & (97)\end{matrix}$

where ε_(r) comprises the relative permittivity and σ₁ is theconductivity of the lossy conducting medium 203 at the location of thereceiving structure, ε₀ is the permittivity of free space, and ω=2πf,where f is the frequency of excitation. Thus, the wave tilt angle (Ψ)can be determined from Equation (97).

The total phase shift (Φ=θ_(c)+θ_(y)) of the tuned resonator 306 aincludes both the phase delay (θ_(c)) through the coil L_(R) and thephase delay of the vertical supply line (θ_(y)). The spatial phase delayalong the conductor length l_(w) of the vertical supply line can begiven by θ_(y)=β_(w)l_(w), where β_(w) is the propagation phase constantfor the vertical supply line conductor. The phase delay due to the coil(or helical delay line) is θ_(c)=β_(p)l_(c), with a physical length ofl_(c) and a propagation factor of

$\begin{matrix}{{\beta_{p} = {\frac{2\; \pi}{\lambda_{p}} = \frac{2\; \pi}{V_{f}\lambda_{0}}}},} & (98)\end{matrix}$

where V_(f) is the velocity factor on the structure, λ₀ is thewavelength at the supplied frequency, and λ_(p) is the propagationwavelength resulting from the velocity factor V_(f). One or both of thephase delays (θ_(c)+θ_(y)) can be adjusted to match the phase shift Φ tothe angle (Ψ) of the wave tilt. For example, a tap position may beadjusted on the coil L_(R) of FIG. 18B to adjust the coil phase delay(θ_(c)) to match the total phase shift to the wave tilt angle (Φ=Ψ). Forexample, a portion of the coil can be bypassed by the tap connection asillustrated in FIG. 18B. The vertical supply line conductor can also beconnected to the coil L_(R) via a tap, whose position on the coil may beadjusted to match the total phase shift to the angle of the wave tilt.

Once the phase delay (Φ) of the tuned resonator 306 a has been adjusted,the impedance of the charge terminal T_(R) can then be adjusted to tuneto resonance with respect to the perfectly conducting image ground planeat complex depth z=−d/2. This can be accomplished by adjusting thecapacitance of the charge terminal T₁ without changing the travelingwave phase delays of the coil L_(R) and vertical supply line. Theadjustments are similar to those described with respect to FIGS. 9A and9B.

The impedance seen “looking down” into the lossy conducting medium 203to the complex image plane is given by:

Z _(in) =R _(in) +jX _(in) =Z ₀ tan h(jβ ₀(d/2)),  (99)

where β₀=ω√{square root over (μ₀ε₀)}. For vertically polarized sourcesover the Earth, the depth of the complex image plane can be given by:

d/2≈1/√{square root over (jωμ ₁σ₁−ω²μ₁ε₁)},  (100)

where μ₁ is the permeability of the lossy conducting medium 203 andε₁=ε_(r)ε₀.

At the base of the tuned resonator 306 a, the impedance seen “lookingup” into the receiving structure is Z_(⬆)=Z_(base) as illustrated inFIG. 9A. With a terminal impedance of:

$\begin{matrix}{{Z_{R} = \frac{1}{j\; \omega \; C_{R}}},} & (101)\end{matrix}$

where C_(R) is the self-capacitance of the charge terminal T_(R), theimpedance seen “looking up” into the vertical supply line conductor ofthe tuned resonator 306 a is given by:

$\begin{matrix}{{Z_{2} = {{Z_{W}\frac{Z_{R} + {Z_{w}\tan \; {h( {j\; \beta_{w}h_{w}} )}}}{Z_{w} + {Z_{R}\tan \; {h( {j\; \beta_{w}h_{w}} )}}}} = {Z_{W}\frac{Z_{R} + {Z_{w}\tan \; {h( {j\; \theta_{y}} )}}}{Z_{w} + {Z_{R}\tan \; {h( {j\; \theta_{y}} )}}}}}},} & (102)\end{matrix}$

and the impedance seen “looking up” into the coil L_(R) of the tunedresonator 306 a is given by:

$\begin{matrix}{Z_{base} = {{R_{base} + {jX}_{base}} = {{Z_{R}\frac{Z_{2} + {Z_{R}\tan \; {h( {j\; \beta_{p}H} )}}}{Z_{R} + {Z_{2}\tan \; {h( {j\; \beta_{p}H} )}}}} = {Z_{c}{\frac{Z_{2} + {Z_{R}\tan \; {h( {j\; \theta_{c}} )}}}{Z_{R} + {Z_{2}\tan \; {h( {j\; \theta_{c}} )}}}.}}}}} & (103)\end{matrix}$

By matching the reactive component (X_(in)) seen “looking down” into thelossy conducting medium 203 with the reactive component (X_(base)) seen“looking up” into the tuned resonator 306 a, the coupling into theguided surface waveguide mode may be maximized.

Referring next to FIG. 18C, shown is an example of a tuned resonator 306b that does not include a charge terminal T_(R) at the top of thereceiving structure. In this embodiment, the tuned resonator 306 b doesnot include a vertical supply line coupled between the coil L_(R) andthe charge terminal T_(R). Thus, the total phase shift (Φ) of the tunedresonator 306 b includes only the phase delay (θ_(c)) through the coilL_(R). As with the tuned resonator 306 a of FIG. 18B, the coil phasedelay θ_(c) can be adjusted to match the angle (Ψ) of the wave tiltdetermined from Equation (97), which results in Φ=Ψ. While powerextraction is possible with the receiving structure coupled into thesurface waveguide mode, it is difficult to adjust the receivingstructure to maximize coupling with the guided surface wave without thevariable reactive load provided by the charge terminal T_(R).

Referring to FIG. 18D, shown is a flow chart 180 illustrating an exampleof adjusting a receiving structure to substantially mode-match to aguided surface waveguide mode on the surface of the lossy conductingmedium 203. Beginning with 181, if the receiving structure includes acharge terminal T_(R) (e.g., of the tuned resonator 306 a of FIG. 18B),then the charge terminal T_(R) is positioned at a defined height above alossy conducting medium 203 at 184. As the surface guided wave has beenestablished by a guided surface waveguide probe 200, the physical height(h_(p)) of the charge terminal T_(R) may be below that of the effectiveheight. The physical height may be selected to reduce or minimize thebound charge on the charge terminal T_(R) (e.g., four times thespherical diameter of the charge terminal). If the receiving structuredoes not include a charge terminal T_(R) (e.g., of the tuned resonator306 b of FIG. 18C), then the flow proceeds to 187.

At 187, the electrical phase delay Φ of the receiving structure ismatched to the complex wave tilt angle Ψ defined by the localcharacteristics of the lossy conducting medium 203. The phase delay(θ_(c)) of the helical coil and/or the phase delay (θ_(y)) of thevertical supply line can be adjusted to make D equal to the angle (Ψ) ofthe wave tilt (W). The angle (Ψ) of the wave tilt can be determined fromEquation (86). The electrical phase D can then be matched to the angleof the wave tilt. For example, the electrical phase delay Φ=_(c)+θ_(y)can be adjusted by varying the geometrical parameters of the coil L_(R)and/or the length (or height) of the vertical supply line conductor.

Next at 190, the load impedance of the charge terminal T_(R) can betuned to resonate the equivalent image plane model of the tunedresonator 306 a. The depth (d/2) of the conducting image ground plane139 (FIG. 9A) below the receiving structure can be determined usingEquation (100) and the values of the lossy conducting medium 203 (e.g.,the Earth) at the receiving structure, which can be locally measured.Using that complex depth, the phase shift (On) between the image groundplane 139 and the physical boundary 136 (FIG. 9A) of the lossyconducting medium 203 can be determined using θ_(d)=β_(o) d/2. Theimpedance (Z_(in)) as seen “looking down” into the lossy conductingmedium 203 can then be determined using Equation (99). This resonancerelationship can be considered to maximize coupling with the guidedsurface waves.

Based upon the adjusted parameters of the coil L_(R) and the length ofthe vertical supply line conductor, the velocity factor, phase delay,and impedance of the coil L_(R) and vertical supply line can bedetermined. In addition, the self-capacitance (C_(R)) of the chargeterminal T_(R) can be determined using, e.g., Equation (24). Thepropagation factor (β_(p)) of the coil L_(R) can be determined usingEquation (98), and the propagation phase constant (β_(w)) for thevertical supply line can be determined using Equation (49). Using theself-capacitance and the determined values of the coil L_(R) andvertical supply line, the impedance (Z_(base)) of the tuned resonator306 a as seen “looking up” into the coil L_(R) can be determined usingEquations (101), (102), and (103).

The equivalent image plane model of FIG. 9A also applies to the tunedresonator 306 a of FIG. 18B. The tuned resonator 306 a can be tuned toresonance with respect to the complex image plane by adjusting the loadimpedance Z_(R) of the charge terminal T_(R) such that the reactancecomponent X_(base) Of Z_(base) cancels out the reactance component ofX_(in) of Z_(in), or X_(base)+X_(in)=0. Thus, the impedance at thephysical boundary 136 (FIG. 9A) “looking up” into the coil of the tunedresonator 306 a is the conjugate of the impedance at the physicalboundary 136 “looking down” into the lossy conducting medium 203. Theload impedance Z_(R) can be adjusted by varying the capacitance (C_(R))of the charge terminal T_(R) without changing the electrical phase delayΦ=θ_(c)+θ_(y) seen by the charge terminal T_(R). An iterative approachmay be taken to tune the load impedance Z_(R) for resonance of theequivalent image plane model with respect to the conducting image groundplane 139. In this way, the coupling of the electric field to a guidedsurface waveguide mode along the surface of the lossy conducting medium203 (e.g., Earth) can be improved and/or maximized.

Referring to FIG. 19, the magnetic coil 309 comprises a receive circuitthat is coupled through an impedance matching network 333 to anelectrical load 336. In order to facilitate reception and/or extractionof electrical power from a guided surface wave, the magnetic coil 309may be positioned so that the magnetic flux of the guided surface wave,H_(φ), passes through the magnetic coil 309, thereby inducing a currentin the magnetic coil 309 and producing a terminal point voltage at itsoutput terminals 330. The magnetic flux of the guided surface wavecoupled to a single turn coil is expressed by

=∫∫_(A) _(CS) μ_(r)μ_(o)

·{circumflex over (n)}dA  (104)

where

is the coupled magnetic flux, μ_(r) is the effective relativepermeability of the core of the magnetic coil 309, μ₀, is thepermeability of free space,

is the incident magnetic field strength vector, {circumflex over (n)} isa unit vector normal to the cross-sectional area of the turns, andA_(CS) is the area enclosed by each loop. For an N-turn magnetic coil309 oriented for maximum coupling to an incident magnetic field that isuniform over the cross-sectional area of the magnetic coil 309, theopen-circuit induced voltage appearing at the output terminals 330 ofthe magnetic coil 309 is

$\begin{matrix}{{V = {{{- N}\frac{d}{dt}} \approx {{- j}\; \omega \; \mu_{r}\mu_{0}{NHA}_{CS}}}},} & (105)\end{matrix}$

where the variables are defined above. The magnetic coil 309 may betuned to the guided surface wave frequency either as a distributedresonator or with an external capacitor across its output terminals 330,as the case may be, and then impedance-matched to an external electricalload 336 through a conjugate impedance matching network 333.

Assuming that the resulting circuit presented by the magnetic coil 309and the electrical load 336 are properly adjusted and conjugateimpedance matched, via impedance matching network 333, then the currentinduced in the magnetic coil 309 may be employed to optimally power theelectrical load 336. The receive circuit presented by the magnetic coil309 provides an advantage in that it does not have to be physicallyconnected to the ground.

With reference to FIGS. 18A, 18B, 18C and 19, the receive circuitspresented by the linear probe 303, the mode-matched structure 306, andthe magnetic coil 309 each facilitate receiving electrical powertransmitted from any one of the embodiments of guided surface waveguideprobes 200 described above. To this end, the energy received may be usedto supply power to an electrical load 315/327/336 via a conjugatematching network as can be appreciated. This contrasts with the signalsthat may be received in a receiver that were transmitted in the form ofa radiated electromagnetic field. Such signals have very low availablepower, and receivers of such signals do not load the transmitters.

It is also characteristic of the present guided surface waves generatedusing the guided surface waveguide probes 200 described above that thereceive circuits presented by the linear probe 303, the mode-matchedstructure 306, and the magnetic coil 309 will load the excitation source212 (e.g., FIGS. 3, 12 and 16) that is applied to the guided surfacewaveguide probe 200, thereby generating the guided surface wave to whichsuch receive circuits are subjected. This reflects the fact that theguided surface wave generated by a given guided surface waveguide probe200 described above comprises a transmission line mode. By way ofcontrast, a power source that drives a radiating antenna that generatesa radiated electromagnetic wave is not loaded by the receivers,regardless of the number of receivers employed.

Thus, together one or more guided surface waveguide probes 200 and oneor more receive circuits in the form of the linear probe 303, the tunedmode-matched structure 306, and/or the magnetic coil 309 can make up awireless distribution system. Given that the distance of transmission ofa guided surface wave using a guided surface waveguide probe 200 as setforth above depends upon the frequency, it is possible that wirelesspower distribution can be achieved across wide areas and even globally.

The conventional wireless-power transmission/distribution systemsextensively investigated today include “energy harvesting” fromradiation fields and also sensor coupling to inductive or reactivenear-fields. In contrast, the present wireless-power system does notwaste power in the form of radiation which, if not intercepted, is lostforever. Nor is the presently disclosed wireless-power system limited toextremely short ranges as with conventional mutual-reactance couplednear-field systems. The wireless-power system disclosed hereinprobe-couples to the novel surface-guided transmission line mode, whichis equivalent to delivering power to a load by a waveguide or a loaddirectly wired to the distant power generator. Not counting the powerrequired to maintain transmission field strength plus that dissipated inthe surface waveguide, which at extremely low frequencies isinsignificant relative to the transmission losses in conventionalhigh-tension power lines at 60 Hz, all of the generator power goes onlyto the desired electrical load. When the electrical load demand isterminated, the source power generation is relatively idle.

Referring next to FIGS. 20A-E, shown are examples of various schematicsymbols that are used with reference to the discussion that follows.With specific reference to FIG. 20A, shown is a symbol that representsany one of the guided surface waveguide probes 200 a, 200 b, 200 c, 200e, 200 d, or 200 f; or any variations thereof. In the following drawingsand discussion, a depiction of this symbol will be referred to as aguided surface waveguide probe P. For the sake of simplicity in thefollowing discussion, any reference to the guided surface waveguideprobe P is a reference to any one of the guided surface waveguide probes200 a, 200 b, 200 c, 200 e, 200 d, or 200 f; or variations orcombinations thereof.

Similarly, with reference to FIG. 20B, shown is a symbol that representsa guided surface wave receive structure that may comprise any one of thelinear probe 303 (FIG. 18A), the tuned resonator 306 (FIGS. 18B-18C), orthe magnetic coil 309 (FIG. 19). In the following drawings anddiscussion, a depiction of this symbol will be referred to as a guidedsurface wave receive structure R. For the sake of simplicity in thefollowing discussion, any reference to the guided surface wave receivestructure R is a reference to any one of the linear probe 303, the tunedresonator 306, or the magnetic coil 309; or variations or combinationsthereof.

Further, with reference to FIG. 20C, shown is a symbol that specificallyrepresents the linear probe 303 (FIG. 18A). In the following drawingsand discussion, a depiction of this symbol will be referred to as aguided surface wave receive structure R_(P). For the sake of simplicityin the following discussion, any reference to the guided surface wavereceive structure R_(P) is a reference to the linear probe 303 orvariations thereof.

Further, with reference to FIG. 20D, shown is a symbol that specificallyrepresents the tuned resonator 306 (FIGS. 18B-18C). In the followingdrawings and discussion, a depiction of this symbol will be referred toas a guided surface wave receive structure R_(R). For the sake ofsimplicity in the following discussion, any reference to the guidedsurface wave receive structure R_(R) is a reference to the tunedresonator 306 or variations thereof.

Further, with reference to FIG. 20E, shown is a symbol that specificallyrepresents the magnetic coil 309 (FIG. 19). In the following drawingsand discussion, a depiction of this symbol will be referred to as aguided surface wave receive structure R_(M). For the sake of simplicityin the following discussion, any reference to the guided surface wavereceive structure R_(M) is a reference to the magnetic coil 309 orvariations thereof.

2. Object Identification 2(A). General Overview

With additional reference to FIGS. 21 and 22, schematically illustratedare embodiments of an object identification system 400 that uses guidedsurface waves as described in the preceding section to power one or moreresponsive tags 402. It will be re-emphasized that the appended figuresare not necessarily to scale.

Each tag 402 may be associated with an object 404. The object 404 may beany type of article. Exemplary objects 404 include, but are not limitedto, a consumer item, a group of goods, an article of clothing, afoodstuff, packaging for an article, a container for multiple articles,a vehicle, a pallet on which goods are stacked, a shipping container, orany other item for which tracking is desired.

The object identification system 400 includes an interrogator 406. Inthe embodiment of FIG. 21, the interrogator 406 includes a guidedsurface wave waveguide probe P and a receiver 408 that are co-located.The probe P and receiver 408 may be housed in the same structure, suchas a radome, decorative enclosure, etc. In this embodiment, theinterrogator 406 typically has a fixed location.

In the embodiment of FIG. 22, the probe P and the receiver 408 are notco-located. As will be described, the probe P and the receiver 408 mayhave a physical relationship (e.g., both may be deployed at a facility)or may have no or very little physical association. In this embodiment,the probe P and receiver 408 functionally form an interrogator 406, butare not necessarily deployed by the same party, need not be co-located,and need not be thought of as a unit. In this embodiment, the probe Ptypically has a fixed location and may be housed in a suitable structuresuch as a radome or decorative enclosure. The receiver 408 may have afixed location or may be portable. For instance, the receiver 408 may behandheld and used by a person as the person moves about or may bemounted on a vehicle such as a truck, fork truck, aircraft, cargo ship,etc.

In the embodiments of FIGS. 21 and 22, the probe P launches a guidedsurface wave along an underlying terrestrial medium 410 as described inthe preceding section. The terrestrial medium 410 may be any appropriatelossy conducting medium such as, but not limited to, the earth, thefloor of a store, warehouse, factory or other facility, or any otherappropriate substrate. As described, the probe P does not produce aradiated wave, but launches a guided surface wave along the surface ofthe medium 410. The energy emitted from the probe P is transmitted asZenneck surface currents to one or more tags 402 that are located withinan effective transmission range of the guided surface waveguide probe P.The probe P may be configured as any of the probes described above or inany other appropriate configuration.

With additional reference to FIG. 23, a representative tag 402 isschematically illustrated. The tag 402 is configured much like an RFIDtag and includes an antenna 412 and tag circuitry 414 that are mountedto a substrate 416, such as a paper or plastic sheet. The substrate 416may include adhesive to attach the tag 402 to the object 404. Otherfastening techniques may be used or the tag 402 may form part of theobject 404. In another embodiment, the tag may be located inside theobject 404 or the electrical components of the tag 402 may form part ofelectrical components of the object 404.

In a typical embodiment, other than the drawing of power from the guidedsurface wave, the tag 402 does not have a power source, such as abattery or a physical connection to an external power source. Rather,the tag 402 is responsive to guided surface waves of one or morefrequencies. For instance, electromagnetic energy from the guidedsurface wave produced by the probe P induces a current in the antenna412 and this current is coupled to and used to power the tag circuitry414. Similar to the way RF energy powers a conventional RFID tag, thepowering of the tag circuitry 414 in this manner may be referred to asilluminating the tag 402. But, in contrast to conventional RFID tags,the tag circuitry 414 may load the probe P.

The tag circuitry 414 may include any appropriate electrical componentsand may be configured to carry out any appropriate functions. Forexample, the tag circuitry 414 may include a memory that stores datasuch as, but not limited to, an identifier that may be used to identifythe associated object 404. The identifier may be representative of thetype of goods, such as a stock-keeping unit (SKU). SKUs are uniqueidentifiers for each distinct product available in commerce.Alternatively, the identifier may be representative of the specificitem, such as a unique identifier that distinguishes the object from allother objects including objects that are nominally the same (e.g.,objects having the same SKU). The tag circuitry 414 may read theidentifier from the memory and, via the antenna 412 (or a secondantenna, not shown) transmit an RF signal containing the identifier in adata message format. In another embodiment, the tag 402 may respond byemitting a guided surface wave, but an RF return signal is likely moreconvenient to generate due to a desire to keep the tags 402 relativelysmall, flat and power efficient.

In one embodiment, the tag is addressable and has a unique address, suchas a media access control (MAC) address or an Internet protocol version6 (IPv6) address, which includes hierarchical addressing. In oneembodiment, the identifier of the tag is the same as the address of thetag.

The RF signal emitted by the tag 402 may be received by the receiver408. The receiver 408 may analyze the signal to determine theidentifier. In one embodiment, the receiver 408 communicates theidentifier and any other appropriate information collected duringreading of the tag 402 to a computer system 418 (FIGS. 21 and 22). Forthese purposes, the receiver 408 may include an antenna and radiocircuit that receive the RF signal emitted by the tag 402, processingcircuitry to conduct any appropriate functions connected with thereading, storing, analyzing and processing of data received from the tag402 or ascertained at the time of reading (e.g., location data, time ofarrival or signal strength as described below), and communicationsinterfaces for establishing operative communication with the computersystem 418. Therefore, the receiver 408 may include a memory for storingdata and logical instructions and a processor for executing the logicalinstructions. Alternatively, the computer system 418 and the receiver408 may be combined.

Upon receipt of the identifier, the computer system 418 may carry outone or more functions appropriate for the received identifier. Variousexemplary functions that are carried out by the computer system 418 willbe described in greater detail below.

The receiver 408 and the computer system 418 may communicate over acommunications medium 420. The communications medium 420 may include oneor more of a direct wired connection (e.g., a USB interface), a directwireless connection (e.g., a Bluetooth interface), a wide area networkconnection (e.g., communications over the Internet) or a local areanetwork (e.g., communications over a corporate network or WiFi network),etc. In some embodiments, the computer system 418 also may communicatewith the probe P, such as to control the generation of the guidedsurface wave in terms of when to generate the guided surface wave, theduration of the guided surface wave production, the frequency of theguided surface wave, etc.

2(B). Powering Tags with a Guided Surface Wave

Powering RFID tags is forward link limited. More specifically,conventional RFID tags are illuminated and read by a conventional RFIDinterrogator (also referred to as an RFID reader). The RFID interrogatoremits an RF signal using a relatively small and directional antenna. Theemitted RF energy is limited, typically by a regulatory authority suchas the Federal Communications Commission (FCC) in the US. The limits arepresent to avoid creating impermissible interference to other systemsand to avoid the emission of potentially harmful radiation. Therefore,to transfer enough energy to a conventional RFID tag using conventionalRFID frequencies (e.g., allocated frequencies near 900 MHz or at 13.56MHz) to power the tag's circuitry and invoke an RF response requiresclose proximity between the conventional RFID interrogator and theconventional RFID tag. In most cases, the maximum distance between theRFID interrogator and the RFID tag for effective reading is a fewmeters, and may be shorter when the return signal from the RFID tagrelies on inductive coupling with the RFID interrogator. In addition,conventional RFID technologies have poor penetration into highpermittivity and lossy materials, an example of which is a pallet ofwater bottles or water-containing foodstuffs. Therefore, reading an RFIDtag where a high permittivity and lossy material is interposed betweenthe RFID interrogator and the RFID tag is often not successful.

Conventional RFID technologies inherently limit the functionality of theRFID tags. More specifically, there is little power available to performprocessing functions, memory read operations, memory write operations,data transmit operations and so forth. At the same time, there isinterest by merchants and others to extend RFID applications forinventory and supply chain control, reducing “shrinkage” of inventorycaused by the theft of product, and carrying out other functions.

The techniques disclosed herein overcome these deficiencies and enhancethe functions that may be carried out with tagged objects by use of aguided surface wave to supply a greater amount of power “on target”(e.g., the target being one or more tags 402). Therefore, the disclosedtechnique overcome the forward link limitations found with conventionalRFID tags.

The tag 402 may be thought of as a load on the probe P and, in mostsituations, may draw as much power as needed to perform processingfunctions, memory read operations, memory write operations, datatransmit operations and so forth. Exemplary operations will be describedin greater detail below. Furthermore, the distance between the tag 402and the probe P and the distance between the tag 402 and the receiver408 may be greatly extended relative to the distance conventionallyrequired between RFID interrogators and RFID tags. It is noted that theforward link to power the tags 402 in the disclosed approach may havetens of dB higher link quality than the return link between the tag 402and receiver 408. Nevertheless, system performance will be satisfactoryto carry out the functions and features described herein as well asother similar features and functions.

In order to derive power from the guided surface wave, the tag 402includes the antenna 412. The antenna 412 may be a loop antenna (alsoreferred to as a coil antenna) as schematically shown in FIG. 23 or maybe implemented as the magnetic coil 309 schematically shown in FIG. 19.In other embodiments, the antenna 412 may be configured as a dipoleantenna or as the linear probe 303 schematically shown in FIG. 18A. Morethan one antenna 412 may be present. In this case, the antennas 412 maybe of the same type (e.g., loop antennas or dipole antennas) or may beof different types (e.g., a loop antenna and a dipole antenna). Presenceof a loop antenna and a dipole antenna that are generally in the sameplane or in parallel planes (e.g., both on the substrate 416) mayfacilitate the powering of the tag regardless of the tag's orientation.This is because at least one of the antennas will better align with themagnetic components of the guided surface wave or the electricalcomponents of the guided surface wave, which are normal to each other.Thus, depending on spatial orientation of the tag, the loop antenna maybe the dominant supplier of electrical power to the tag circuit 414 fromthe magnetic components of the guided surface wave or the dipole antennamay be the dominant supplier of electrical power to the tag circuit 414from the electrical components of the guided surface wave. It is furthercontemplated that many conventional RFID tag antenna designs may beemployed or modified to convert enough energy from the guided surfacewave to electrical energy to power the tag circuit 414.

The tag circuitry 414 may include an impedance matching network asdescribed above. In some embodiments, the impedance matching networkwill be statically arranged or may be omitted. A statically arranged oromitted impedance matching network may not result in maximum energyconversion performance, but will make the tag circuitry 414 relativelysimple and accommodate frequent movement of the tag 402 without the needto reconfigure the impedance matching network according to its locationrelative to the lossy conducting medium 410. Regardless of the specificarrangement of the antenna 412, the tag 402 may be considered to includea guided surface wave receive structure R as described above inconnection with FIGS. 1-20E.

The tag 402 may be relatively small and light. Most tags 402 will besimilar in size and weight to conventional RFID tags. For example, thetag 402 may be relatively flat (e.g., about 1 mm thick or less), in therange of about 1 cm long to about 10 cm long, and in the range of about1 cm wide to about 10 cm wide.

As will be described, the guided surface wave that functions as aforward link to deliver power from the probe P to the tag 402 may haveone frequency and the tag 402 may emit a return link signal on a secondfrequency to transmit data to the receiver 408. To increase performanceand data throughput for multiple tags 402 operating at low power, thesecond frequency may be higher than the first frequency (e.g., one ormore orders of magnitude higher). To accommodate the emission of thereturn link signal at high frequencies, the tag 402 may include a secondantenna 422 in cases where the antenna 412 is not capable of efficientlyemitting the return link signal.

The system 400 may be configured to take advantage of the properties ofguided surface waves as described above. Thus, practical use of a guidedsurface wave at a relatively low frequency may be made in connectionwith object identification. In one embodiment, the frequency of theguided surface wave emitted by the probe is around 13.56 MHz or otherfrequency that is already authorized by the appropriate regulatoryauthority for use with RFID technology. Frequencies higher than or lowerthan 13.56 MHz may be used depending on the object identificationapplication and desired characteristics of the guided surface wave. Thearchitecture of the tag 402, including antenna configuration and/orimpedance matching, may be coordinated with the frequency of the guidedsurface wave to effectuate energy transfer.

As described above, field strength of the guided surface wave remainsrelatively high for distances from the probe P that are less than theknee 109 (FIG. 1) of the guided field strength curve 103. As such, asingle probe P may be used to power many tags 200 within an effectivearea surrounding the probe P while maintaining an acceptable energydensity at the location of the probe P. For instance, effectiveisotropic radiated power (EIRP) at the energy source used in connectionwith object identification applications may be imposed by regulatoryauthorities. Typical limits for conventional RFID applications are aboutone or two watts. One might reasonably assume that these types of EIRPlimits will be maintained for some types of object identificationapplications using guided surface waves. Even at these limits, a singleprobe P may be able to power hundreds, thousands or millions of tags 402that are located within a radial distance from the probe P that is lessthan the distance of the knee 109 of the corresponding guided fieldstrength curve 103 from the probe P. For an omnidirectional probe P, theeffective area in which tags may be illuminated is a circular area havea radius that is about the distance of the knee 109 of the correspondingguided field strength curve 103 from the probe P. The distance of theknee 109 from the probe P is dependent on frequency of the guidedsurface wave. As an example, the distance of the knee 109 from the probeP for a guided surface wave at about 13 MHz is approximately onekilometer, depending on ground properties. Under relatively idealcircumstances, conventional RFID technology operating at 900 MHz has aneffective operating range of about 30 meters. Therefore, it will beappreciated that tags 402 may be powered from a much greater distanceand at a much lower frequency than previously possible.

A tag 402 may be configured to respond (e.g., become powered and/ortransmit a return signal) when illuminated with a guided surface wave ofa predetermined frequency, multiple frequencies or a range offrequencies. In one embodiment, a tag 402 is configured to respond to afirst frequency, but not a second frequency, and a different tag 402 isconfigured to respond to the second frequency, but not the firstfrequency. In one embodiment, a minimum separation between the first andsecond frequencies may be established, such as about a 10 kHz separationor a 100 kHz separation.

As will be appreciated, many tags 402 may be powered efficiently withthe use of a guided surface wave and the tags 402 may be configured tocarry out relatively power intensive functions. Many of these functionswill be described below. Moreover, the use of inductive readers withlimited operational range may be avoided. This allows for theinterrogation of tags 402 at a significant distance and/or withrelatively low frequencies. The nature of guide surface waves alsoallows for the interrogation of a tag 402 in situations where highpermittivity material and/or lossy material is interposed between theprobe P and the tag 402. As an example, a tag 402 located within apallet of goods or a shipping container of goods having water content(e.g., water-containing foodstuffs such as water bottles, beer, soup,condiments such as ketchup or barbeque sauce, etc.) may be interrogated.In one embodiment, a tag 402 may be powered to operate when there is oneto five meters of water interposed between the probe P and the tag 402.

2(C). Tag Interrogation

One or more tags 402 may be interrogated (also referred to as read) byilluminating the tag 402 with a guided surface wave having a frequencycompatible with the tag 402 and receiving a return signal from the tag402 with a receiver 408. As part of this process, the tag 402 drawspower from the guided surface wave to power the electronics (tag circuit414) in the tag 402. The drawing of power may be a passive operation.Specifically, the guided surface wave induces a current in the antenna412 that is applied to the tag circuitry 414. The application of powerto the tag circuitry 414 activates the tag circuitry 414 to carry outone or more predetermined functions. An exemplary predetermined functionis to read the tag identifier associated with the tag 414 from a memorycomponent of the tag circuit 414 and transmit a return signal containingthe tag identifier. The return signal may be in the form of a datatransmission that follows a predetermined protocol in terms of time oftransmission (e.g., a predetermined time slot under time divisionmultiplexing with the return signals of other tags), electriccharacteristics, message format or content, encryption, etc. The signalmay be received by a receiver 408 and interpreted.

In one embodiment, the return signal may be an RF signal. Thepropagation capabilities of the return signal will depend on thecharacteristics of the RF signal, such as energy level, data encodingand frequency. The distance at which the return signal may beeffectively detected by a receiver 408 will depend on the propagationcapabilities of the return signal in the surrounding environment and thesensitivity of the receiver 408. To enable reading at relatively largedistances, such as greater than 30 meters, the return signal may beemitted with a relatively large EIRP. Drawing power from a guidedsurface wave will allow a transmitter in the tag circuit 414 to radiatewith relatively high power since the energy density of power availablein the source (the guided surface wave) is high. Additionally, thereturn signal may have a frequency that is relatively high to enhancethroughput. In one embodiment, the return signal may have a frequencyhigher than the frequency of the illuminating guided surface wave, suchas about one to three orders of magnitude higher than the frequency ofthe guided surface wave. For example, if the guided surface wave is inthe range of about 10 MHz to about 250 MHz, the return signal may be inthe range of about 100 MHz to about 5.4 GHz, or higher.

Therefore, the guided surface wave may be at one frequency (e.g., afirst frequency) and the tag 402 may respond at a second frequency thatis different than the first frequency. In other embodiments, theresponse frequency may be nominally the same as the guided surface wavefrequency. In one embodiment, a first set of tags 402 responsive to aguided surface wave at a first frequency may respond at a secondfrequency and a second set of tags 402 responsive to a guided surfacewave at the first frequency may respond at a third frequency differentthan the second frequency. Using the difference in response frequencies,the tags of the first set may be distinguished from the tags of thesecond set.

As indicated, one or more predetermined functions may be carried out bythe tag 402 when the tag circuitry 414 becomes activated. One exemplarypredetermined function is to emit a return signal. The return signal maycontain information, such as one or more of an indication that the tag402 is present with no identifying information, an indication of thetype of tag 402 or the type of object 404 with which the tag 402 isassociated, a SKU or other identifier for the object 404 with which thetag 402 is associated, a unique identifier or address of the tag 402that distinguishes the tag 402 from other sets of tags 402 or from allother tags 402, or any other data stored by the tag 402.

In one embodiment, the transmission of the return signal is automatic.In other embodiments, the response or other action taken by the tag 402may be carried out under certain conditions. In an exemplary embodiment,the tag 402 is addressable and responds to messages or data addressed tothe tag 402. Depending on the addressing scheme, the tag 402 may beindividually addressable. For this purpose, the tag 402 may have anyaddress that is unique from the addresses of all other tags 402, such asan IPv6 address or some other address of appropriate format. In oneembodiment, the address may have a length that is about 40 bits to about64 bits. It is contemplated that addresses that are 64 bits long orlonger may be used to uniquely address every object on the planet. Inother embodiments, a message or command may be addressed to plural tags402. For this purpose, tags 402 may share a common address (e.g., alltags 402 associated with a SKU may have the same address) orhierarchical addressing may be used to take advantage of otherwiseunique addresses. Other exemplary data distribution techniques includemulticast addressing or geocasting.

Using addressable tags 402 allows for various predetermined functions tobe carried out by the tags 402. As an example, a data link orcommunications interface (e.g., Bluetooth interface) between thereceiver 408 and the tag 402 may be established for the bidirectionalexchange of data. Communication between the receiver 408 and the tag 402may allow the receiver 408 (or the computer system 418 via the receiver408) to poll the tag 402 for information stored by the tag 402 or sendcommands to the tag, or may allow the tag 402 to receive and storeadditional information.

In another embodiment, the predetermined function that is carried out bythe tag 402 includes storing data encoded in the guided surface wave orcarrying out a command that is encoded in the guided surface wave. Thedata or command in the guided surface wave to which the tag 402 isresponsive may be broadcast to tags 402 without addressing or may beaddressed to one or more specific tags 402. For this purpose, the probeP may include an encoded carrier message in the guided surface wave.

Predetermined functions that may be carried out by one or more tags 402when data and/or commands are transmitted by the receiver 408 or as partof the guided surface wave may include, but are not limited to, writingdata to a memory of the tag 402, executing a command, responding withrequested information, and responding by emitting a return signal onlyif addressed or otherwise polled.

Another predetermined function may be to stop emitting the return signalin response to a message acknowledging receipt of the return signal oran appropriate command. This function may be employed in varioussituations. For instance, during an inventory control operation, theguided surface wave may be used to illuminate many tags 402, all ofwhich may commence response operations by emitting respective returnsignals. As responses from individual tags 402 are received andprocessed, the computer system 418 may issue commands (via the receiver408 or the guided surface wave) to the tags 402 from which returnsignals are received and processed to stop emitting return signals. Inthis manner, the return signals from other tags 402 may be received andprocessed with less contention.

In one embodiment, it may be possible to permanently “turn off” ordeactivate a tag 402 by executing a command in the tag 402. Forinstance, after an object 404 is purchased by a consumer, its associatedtag 402 may be deactivated so that the tag will no longer carry outpredetermined functions when illuminated by an appropriate guidedsurface wave.

2(D). Regionalizing Tag Illumination

Additional reference is made to FIG. 24. FIG. 24 shows two adjacentsites 424 a and 424 b. The sites 424 in the illustrated embodiment arebuildings that each house a retail establishment. This exemplaryembodiment is shown for descriptive purposes. It will be appreciatedthat the illustrated embodiment is representative of aspects of thedisclosed concepts. The nature and configuration of sites at whichprinciples of the disclosed concepts are applicable may vary. Types ofsites include, but are not limited to, retail establishments,warehouses, office facilities, schools, ports, fulfillment centers,shipping and sorting centers, sporting venues, parking lots, factory ormanufacturing establishments, farms, military bases, etc. The sites maynot include any building structures or may include one or more buildingstructures. Each site is characterized by a known geographical area inwhich the illumination and reading of tags 402 is desired. Due to therelative size of the tags 402 and the sites, individual tags 402 andassociated objects 404 are not shown in FIG. 24 for simplicity ofillustration. But it will be understood that tags 402 and associatedobjects 404 are present within each site 424. The number of tags 402 andassociated objects 404 in a site 424 may vary and could range from aslittle as one tag 402/associated object 404 to millions of tags402/associated objects 404.

In the illustrated embodiment, the sites 424 a and 424 b are spacedapart. Adjacent sites 424 need not be spaced apart. Sites 424 thatcorrespond to buildings may touch or nearly touch one another, or mayshare a wall that demarks one site 424 from another.

In one embodiment, a probe P is associated with each site 424.Typically, the probe P is located within the geographic area thatdefines the site 424. One or more receivers 408 are also associated withand located at the site 424. Typically, the receivers 408 that areassociated with a site 424 are located within the geographic area thatdefines the site 424, but one or more of the receivers 408 associatedwith a site 424 may be located outside this geographic area such as nearan entrance to the site 424.

Each probe P is configured to illuminate tags 402 located within thegeographic area of the site 424 associated with the probe P. In oneembodiment, the probe P associated with one site 424 is configured tonot illuminate tags 402 that are located within an adjacent site 424. Itwill be appreciated that not illuminating tags 402 in an adjacent sitemay not always be possible or practical, and/or sometimes tags 402 in anadjacent site may be inadvertently illuminated even if care is taken tolimit the operable range of a probe P.

For the purpose of configuring a probe P to not illuminate tags 402 inan adjacent site, the natural “energy bubble” resulting from thegeneration of the guided surface wave by the probe P may be employed. Asdescribed above, the energy density roll-off of a guided surface wave isvery low at distances less than the distance of the knee 109 from theprobe P. At distances at the knee 109 and outward, the energy densityfalls of dramatically. The energy density behaves in this manner in allradial directions from the probe P assuming that the probe P isomnidirectional and the electrical properties of the terrestrial medium410 are uniform along the operative interface between the probe P andthe terrestrial medium 410. The distance of the knee 109 is a functionof the frequency of the guided surface wave. Also, for purposes of thisdescription, to be considered illuminated, a tag 402 must be in thepresence of a threshold energy density to draw sufficient power from theguided surface wave to be powered on and capable of responding. Thethreshold energy density may depend on the energy consumptioncharacteristics of the tag 402 and, therefore, may vary.

For tags 402 that are operatively compatible with the frequency of aguided surface wave generated by a probe P, the area surrounding theprobe P in which the tags 402 will be exposed to the threshold energydensity to become illuminated will be referred to as an illuminationarea 426. As illustrated in the exemplary embodiment of FIG. 24, thereis one illumination area 426 a associated with the site 424 a and probePa and another illumination area 426 b associated with the site 424 band probe Pb. In an embodiment where the frequency of the guided surfacewaves generated by the probes Pa and Pb for neighboring sites 424 a, 424b are operatively compatible with the tags 402 used in the other of theneighboring sites 424 a, 424 b, the establishment of non-overlappingillumination areas 426 will allow for each site 424 to conduct objectidentification by reading tags 402 independently of one another.

In particular, the guided surface wave generated by the probe Pa forsite 424 a will tend not to illuminate tags within the neighboring site424 b and vice versa. Additional precautions may be taken to avoidhaving receivers 408 for one site 424 a detect the responsive signalsfrom tags 402 located in the neighboring site 424 b when the tags 402are illuminated by the probe Pb for the neighboring site 424 b and viceversa. These precautions may include controlling the timing ofillumination so that the probes Pa, Pb from the respective sites 424 a,424 b are not actively generating guide surface waves at the same time.Another precaution is limiting the output power of the tags 402 to alevel low enough to avoid detection by receivers 408 in the other siteand/or limiting the receive sensitivity of the receivers 408 to avoiddetection of signals from tags 402 in the neighboring site 424. Anotherprecaution is maintaining, in a computer system 418 that processesinformation from the readers 408 of a site 424, a database of the tagidentifiers for all the tags 402 that should be present in the site 424.If a tag 402 is read and the associated tag identifier is not in thedatabase, an assumption may be made that the tag 402 is not associatedwith the site 424 and should be ignored. An exception may be made in anintake mode when objects arrive at the site 424 and are interrogated toadd the corresponding tag identifiers to the database.

Noting the foregoing, there are several factors that control theeffective size of the illumination area 426, including power andfrequency of the guided surface wave and the power requirements of thetag 402. Therefore, each of power and frequency of the guided surfacewave, the characteristics of the tags 402 used within the site 424, andthe characteristics of the tags 402 used in neighboring site(s) may beselected in coordination with each other to establish an appropriatesize for each illumination area 426. It will be appreciated, however,that frequency is the most significant contributing factor to size ofthe illumination area 426. A frequency in the range of about 100 MHz toabout 200 MHz should be sufficient to control the size of theillumination area 426 to closely match the size of the site 424 when thesite 424 is a typical warehouse or retail establishment.

It also may be desirable to control the shape of the illumination area426. Shape of the illumination area 426 may be controlled by using aprobe assembly with output that varies as a function of direction. Thismay be achieved using plural probes P to create lobes in the guidedsurface wave profile or create a guided surface wave that is theaggregate of plural directionally launched guided surface waves (e.g., amulti-beam approach). For instance, super-positioning of individualprobes P may be used to make a phased array probe with directionaloutput that is controlled by the presence of multiple, simultaneouslygenerated guided surface waves.

By selecting characteristics of the probe P (or probe assembly) and tags402 to control the size and shape of the illumination area 426, theillumination area 426 may be made to approximate the geographic area ofthe associated site 424. Also, as described above, it may be possible touse one probe P in the site 424 to illuminate all tags 402 in the site424 (e.g., by achieving high energy density across the entire site 424)while maintaining an acceptable energy density at the source (e.g., anEIRP of about 1 watt to about 2 watts at the probe P).

Additional considerations may be used in selecting the frequency of theguided surface wave. For instance, access to certain frequencies may ormay not be made available for object identification purposes by theregulatory authority overseeing the jurisdiction in which the site 424is located.

Another consideration is effective height of the guided surface wave.Energy density of a guided surface wave falls off at a height of about awavelength of the guided surface wave. Therefore, the height of theillumination area 426 will be about a wavelength of the guided surfacewave. For a guided surface wave of about 13 MHz, the probe P will beabout three feet tall and the illumination area 426 will be about 72feet tall (about 22 meters). This height may be sufficient to illuminatetags 402 associated with objects 404 that are placed on upper shelves inmany warehouses. For a guided surface wave of about 100 MHz, theillumination area 426 will be about 3 meters tall and, for a guidedsurface wave of about 300 MHz, the illumination area 426 will be about 1meter tall. These heights may be compatible with many retailenvironments.

2(E). Data Collect from Tags at a Site

Various functions may be carried out by reading tags 402 that arepresent at a site. Exemplary functions include inventory control,finding misplaced objects 404, reducing theft, and consumer transactionoperations. For these tasks, it will be assumed that each object 404 tobe tracked is associated with a tag 402 and the computer system 418maintains a database of the objects 404 and each associated tagidentifier. This information may be generated and/or gathered when thetag 402 is first associated with the object 404, which may occur at alocation remote from the site 424 such as at a factory where the objectis manufactured. In other situations, this information may be generatedand/or gathered when the tag 402 arrives at the site.

To carry out reading of tags 402 at the site 424, one or more probes Pand one or more receivers 408 are present. Since tags 402 may beilluminated by a guided surface wave generated by a probe P that islocated outside the site 424, the probe P need not be located within thegeographic area of the site 424. But it is contemplated that eachreceiver 408 that receives return signals from tags 402 located at thesite 424 will be located in the geographic area of the site 424 or closeto the site 424 (e.g., within a distance capable of receiving returnsignals emitted by tags 402 in the site 424).

Each receiver 408 for a site 424 may be strategically placed, such as bydoors, loading docks, cash registers, etc. For example, in theillustrated embodiment of site 424 a where site 424 a is a retaillocation, a receiver 408 is located adjacent a main entrance 428 thoughwhich customers enter and exit, a receiver 408 is located adjacent adoor 430 that separates a main shopping area 432 from an inventorystorage area 434, and a receiver 408 is located adjacent an ancillaryexit door 436 at the storage area 434. Another receiver 408 may belocated adjacent a loading dock 438 and another receiver 408 may belocated at a payment area 440. Objects 404 and associated tags 402 maybe present on shelves 442 or displays located in the shopping area 432.Additional objects 404 and associated tags 402 may be present on shelves442 or in other locations in the storage area 434. Receivers 408 atadditional or alternative locations also may be present.

With additional reference to the illustration of the exemplary site 424b in FIG. 24, another arrangement for the receivers 408 will bedescribed. In this embodiment, receivers 408 are placed at strategiclocations but are not associated with specific locales within the site424 b such as doors, loading docks, payment areas, etc. Rather, thereceivers 408 are positioned to detect return signals emitted by tags402 that are within the site 424. Although two receivers 408 areillustrated in the appended figure, other numbers of receivers 408 arepossible. For example, there may be only one receiver 408 or three ormore receivers 408. The return signals may be used and analyzed in thesame manners as described above. The number and positioning of receivers408 in either the embodiment of site 424 a or site 424 b may depend onthe operative range between tags 402 and receivers 408, the size of thesite 424, programming of the computer system 418 and any other relevantfactors. Also, the receiver arrangement of the embodiment of site 424 amay be combined with the receiver arrangement of the embodiment of site424 b so that some receivers are positioned in connection with certainstructural elements of the site and others are positioned at moregeneric strategic locations.

It will be recognized that the locations of the receivers 408 in FIG. 24are exemplary and for descriptive purposes. The number and location ofreceivers 408 may be modified depending on the characteristics of thesite 424 and tag reading functions to be performed.

The probe P may be located in a strategic location, but may be hiddenfrom sight. For example, in the embodiment of site 424 a, the probe Pais hidden in an end cap 444 of one of the shelves 442. The probe P maybe configured to generate the guided surface wave continuously so thateach tags 402 in the respective illumination region 426 respondscontinuously, such as by retransmitting the return signal without delaybetween retransmissions or periodically retransmitting the return signal(e.g., once a second). In other embodiments, the probe P is controlledto generate the guided surface wave at desired times and for desireddurations. The desired times may be prescheduled or may be the result oftriggering the activation of the probe (e.g., an operator may triggerthe probe to conduct an inventory check, to find a misplaced object orto tally objects for purchase as described in the following exemplaryfunctions).

The return signals may be detected by one or more receivers 408. Dataderived from the return signals (e.g., the tag identifiers), togetherwith the known locations and/or identities of the receivers 408 thatdetect the return signals, may be used in connection with variousfunctions. One exemplary function is to assist in identifying objects404 that a customer intends to purchase. For instance, a customer maybring objects 404 for purchase to the payment area 440. In theembodiment of site 424 a, the objects 404 may be moved passed thereceiver 408 at the payment area 440 and those objects 404 may be loggedby the computer system 418. It is noted that there is no need for theitems for purchase to be read one at a time in similar manner to the wayprinted SKUs are serially scanned with a bar code reader. Rathermultiple objects 404 may be brought past the receiver 408 at the sametime. Once the objects 404 are identified, the customer may then pay forthe items in the conventional manner.

In another embodiment, information about inventory at the site 424 maybe tracked. For example, in the embodiment of site 424 a, as objects 404enter or leave the site 424, the associated tags 402 may pass by one ofthe receivers 408 located at the door 428, the door 436 or the door 438.By keeping track of the objects 404 that pass these receivers 408, anaccurate tally of the number of objects 404 by object type may be madeand detection of the object moving from an authorized area to anunauthorized area made be made. This detection also may be made bydetecting movement past a predetermined point or crossing a boundarybetween an authorized area and the unauthorized area. In anotherembodiment, detection that an object has left an authorized area may bemade by failing to receive a return signal from the associated tagwithin a predetermined amount of time since the receipt of a lastiteration of the return signal. Also, this information may be crossreferenced against valid object purchases and other valid reasons why anobject may be removed from the site 424 (e.g., shipped to a downstreamlocation in a supply chain or returned to a supplier). If the departureof an object 404 is not associated with a valid reason, then additionalsecurity-related actions may be carried out, such as alerting anauthority (e.g., a manager of the site 424 or the police), turning on asecurity camera and recording video of the area surrounding the door ordock through which the object exited, launching an investigation, etc.

Other information may be determined from the manner in which an object404 enters or exits the site 424, the time of receipt of the returnsignal, and/or additional information such as when a particular vehicleor worker was also present. For example, in a facility with multipleloading docks, tracking the dock through which an object moves may beused to establish which employee handled an object, which truck anobject was loaded onto or which truck brought an object to the facility.As another example, tracking of objects 404 located in the storage area434 versus the shopping area 432 may be made by the receipt of returnsignals by the receiver 408 at the door 430. Other data collectionregarding movement of objects within the site 424 may be made, such astracking movement from one user-defined zone to another user-definedzone, collecting data regarding the behavior of customers, etc.

In another embodiment, an inventory of all objects 404 or certaincategories of objects in the site 424 may be made by analyzing returnsignals from the tags 402. In one embodiment, the computer system 418may analyze the tag identifier associated with each distinct returnsignal to conduct an inventory analysis. In one embodiment,de-interleaving techniques may be applied to ignore or turn off returnsignals from tags 402 having associated tag identifiers that have beenlogged into the inventory analysis. To limit the number of tags 402 thatrespond during an inventory analysis, addressed commands to emit areturn signal may be sent to the specific tags 402 of interest.De-interleaving and/or addressing tags to respond or not respond may beused in conjunction with the other functions described herein.

In one embodiment, the geo-location of all objects 404, certaincategories of objects 404 or a single specific object 404 may beidentified using the return signals from the tags 402 associated withthe objects 404. The location of a tag 402 and its associated object 404may be determined by illuminating the tag 402 and receiving the returnsignal at two or more receivers 408 that each have a known location. Fortwo or more return signals from the same tag 402, time difference ofarrival or differences in received power (e.g., voltage standing waveratio or VSWR) may be used to triangulate the location of the tag 402.This analysis may be repeated for the return signals received frommultiple tags 402. Also, de-interleaving techniques may be applied toignore or turn off return signals from tags 402 for which locations havebeen determined. Also, to limit the number of tags 402 that respondduring a location analysis, addressing may be used to control which tagor tags 402 emit a return signal.

A location determination technique (e.g., the foregoing triangulationtechniques) may be used in conjunction with various functions. Forinstance, with reference to the exemplary depiction of site 424 b, bulkidentification of objects 404 in a particular area may be made. Forexample, there may be a reading zone 446 that serves as a designatedinterrogation area through which items for purchase travel beforeexiting the site 424 b. All of the objects 404 in the dedicated readingzone 446 may be detected by analyzing return signals from tags 402located in the reading zone 446. Therefore, a group of objects may bemoved through the reading zone 446, collectively identified and loggedby the computer system 418. Then a transaction may be completed topurchase the items. This approach to bulk object identification may beapplied in other contexts, such as identification of all items movingthrough a loading dock, identification of all items on a truck or railcar as the truck or rail car moves through a predetermined area, etc.

As another example, geo-location may be used to detect unauthorizedmovement of an object 404 (e.g., theft of the object 404). In oneembodiment, this detection may be made if an object 404 is determined tobe in a location where it should not be present (e.g., the location ofthe object 404 is detected to be outside the geographic area of the site424). In another embodiment, this detection may be made if an objectmoves more than a threshold distance and in an unauthorized directionfrom a predetermined point. This technique may detect an object movingaway from a door and toward a parking lot, for example. Once a detectionof possible unauthorized movement is made, the detection may be crossreferenced against any legitimate reasons for the movement such aspurchase of the object, scheduled shipping of the object to anotherlocation, etc. If no legitimate reason is present for the detectionhaving been made, then security measures may be triggered. The securitymeasures may include, but are not limited to, alerting an authority(e.g., a manager of the site 424 or the police), turning on a securitycamera and recording video of the area surrounding the door or dockthrough which the object exited, launching an investigation, etc.

In another embodiment of determining geo-location of an object 404, thegeo-location of the receiver 408 may be used as a proxy for the locationof the object 404 for which an associated tag return signal is received.For example, if the receiver 408 at the payment area 440 detects thereturn signal for a tag 402, the associated object 404 will be assumedto be located at or near the payment area 440. In the event that morethan one receiver 408 detects the return signal for a tag 402, then thelocation of the receiver 408 that detects the highest signal strengthfor the return signal may be used as a proxy for the location of theassociated object. In some embodiments, the receiver 408 may be mobile,such as a receiver 408 that is mounted on a truck, ship, train or othervehicle. In this case, the geo-location of the receiver 408 that servesas a proxy for the geo-location of the tag 402/object 404 may bedetermined using, for example, global positioning system (GPS)technology.

Any of the foregoing approaches for determining the geo-location of thetag(s) 402 may include the determination of the elevation of the tag(s)402 in addition to geo-location (e.g., as expressed by two dimensionalcoordinates). Also, in some embodiments, it may be possible to refinethe locating of tags 402 by steering the guided surface wave such thatthe guided surface wave only illuminates tags 402 in certain areas ofthe site 424 at a time (e.g., by using a multi-beam guided surface wavegeneration approach to output a guided surface wave that changes indirection over time).

Storing objects in a facility (e.g., warehouse, fulfillment center,storage area of a retail store, etc.) typically involves detailedplanning of where objects are to be placed so that they may be readilyfound when desired. Using the disclosed techniques for illuminating andgeo-locating tags 402, less planning may be employed. Instead, objects404 may be placed in any location that will accommodate the objects 404.This location may be determined at the time of placement using one ofthe foregoing approaches for determining the geo-location of the tag(s)402 that are associated with the objects 404. This location may bestored in a database by the computer system 418 and used to facilitateretrieval of the objects 404 at a later time. Alternatively, the objects404 may be placed in a suitable location without determining or storinginformation about the location. When the objects are desired to befound, one of the foregoing approaches for determining the geo-locationof the tag(s) 402 that are associated with the objects 404 may be usedto determine the location of the objects 404.

In one embodiment, the movement of an object 404 may be tracked byperiodically or continually making location determinations of thegeo-location of the tag 402 that is associated with the object 404.Movement tracking in this manner may be used for inventory planning, formonitoring for theft or product shrinkage, and for a variety of otherpurposes. In one embodiment, the tracking of plural tags 402 may provideadditional information. For instance, if a person is associated with afirst tag 402 and an object 404 is associated with a second tag 402 andthe tags are found to move together, a determination may be made thatthe person is moving the object or is associated with the movement ofthe object (e.g., both are moving together in a vehicle). The sameanalysis may be made for tags 402 associated with vehicles and tagsassociated with objects 404.

A tag 402 may be associated with a person in a number of manners and fora variety of purposes. In one embodiment, a tag 402 that is associatedwith a person may take the form of, or is included in, an objectregularly carried by the person, such as a tag 402 that is similar inform factor to a credit card or a tag 402 that is part of an electronicdevice (e.g., mobile phone or case therefor). Once a tag 402 isassociated with a person, identifying the tag, and hence the person, maybe used for a variety purposes. For instance, a tag 402 that isassociated with a person may be detected at the payment area 440 inconnection with the detection of tags 402 associated with objects thatthe person intends to purchase. If a bank account, credit card or otherpayment means is further associated with the tag 402 that is associatedwith the purchasing person, then payment for the objects 404 may be madeby the computer system 418 registering a transaction using the paymentmeans that is associated with the tag 402 that is associated with thepurchasing person.

In another embodiment, employees at the site 424 may be required tocarry a tag 402. Using location tracking and/or associations of objects404 with the person, a variety of functions may be carried out by thecomputer system 418. Exemplary functions may include tracking taskcompletion, tracking job performance, tracking worked hours, andmonitoring for theft of objects 404 by the employees.

2(F). Macro Illumination of Tags

The previous section described the use of guided surface waves toilluminate tags 402 in a well-defined geographic area corresponding to aknown venue that is typically controlled by one party.

Another embodiment will be described in connection with FIG. 25. In thisembodiment, a guided surface wave may be used to illuminate tags 402over areas in which there may be multiple sites 424, over areas in whichmultiple receivers 408 controlled by respective parties are present,and/or over areas in which tags 402 may travel by vehicle (e.g., truck,car, plane, train, ship, etc.). The areas may include arbitrary areas,paths along which goods are intended to travel, postal codes, cities,counties, states or provinces, countries, continents, or an areadetermined by the operator of the probe P that may or may not correspondto regulatory boundaries, governmental boundaries or geographicboundaries. In one embodiment, the guided surface wave may be producedto illuminate tags 402 on a global basis (i.e., world-wide). Due to thesize of the tags 402 and receivers 408 relative to the size of some ofthe contemplated areas, individual tags 402 and receivers 408 are notshown in FIG. 25 for simplicity of illustration.

Noting that the probe P is not drawn to scale and may be located almostanywhere on the planet, the representative embodiment illustrated inFIG. 25 contemplates a guided surface wave that is capable ofilluminating tags 402 on a global basis. Aspects of the followingdescription, however, also will apply to a smaller illuminated area.

The guided surface wave preferably has a known, fixed frequency (e.g., afirst frequency). One or more additional probes P may be used togenerate a guided surface wave(s) that illuminates tags in at least anarea overlapping the area in which tags 402 are illuminated by theguided surface wave of the first frequency. The other guided surfacewave(s) may have a frequency different than the first frequency andfunctions carried out in connection with the illumination of tags 402with the other guided surface wave(s) may be the same or similar to thefunctions carried out in connection with the illumination of tags 402with the guided surface wave of the first frequency. Therefore, theillumination of tags 402 over relatively wide-spread areas will bedescribed in the context of a single guided surface wave of the firstfrequency and further in the context of tags 402 that are operationallycompatible with the first frequency (e.g., are powered by the guidedsurface wave of the first frequency and are capable of emitting a returnsignal when powered on). The operation of guided surface waves of otherfrequencies and tags that are compatible with those other frequenciesmay be carried out in the same manner and in parallel with the operationof the guided surface wave of the first frequency and tags compatiblewith the first frequency.

In general, as the area in which tags 402 may be powered by the guidedsurface wave of the first frequency increases, the first frequency willdecrease.

Entities that are interested in using the guided surface wave of thefirst frequency and generated by the probe P to power tags 402 maydeploy tags 402 that are compatible with the first frequency. Deployingtags 402 may include, for example, physically associating a compatibletag 402 to each object 404 that the entity wishes to track and loggingthe identity of the object 404 and associated tag identifier in anappropriate database at a computer system 418 (shown not to scale).Physically associating a tag 402 and an object 404 may include adheringor securing the tag 402 directly to the object 404, to the packaging forthe object 404 or some other item that is retained with the object 404(e.g., a manual). In other embodiments, the tag 402 may be inside theobject 404 or an integral part of the object 404.

The entities also may deploy receivers 408 in strategic locations in thearea in which the guided surface wave will illuminate the tags 402. Inaddition to or instead of deploying its own receivers, an entity maycooperate with another party that deploys receivers. The other party mayprovide information (e.g., tag identifiers) present in return signalsdetected by receivers to the entity. The providing of information may bethrough the computer system 418 and may include processing the data tomake various determinations, such as route tracking. It will further beappreciated that there may be multiple computer systems 418 that processinformation from return signals. For example, each entity that isinterested in using the guided surface wave of the first frequency toidentify objects may deploy a computer system 418 or multiple computersystems 418 to process information for multiple sites.

It is contemplated that wide-area illumination of tags 402 will lead toa number of object identification and tracking functions that are notcurrently possible with conventional RFID technology. In addition, anyof the operations carried out when using a local probe P (e.g., asdescribed in connection with the embodiments of FIG. 24) also may becarried out using a remote probe P as described in connection with FIG.25.

Similar to the operations described above, tags 402 that are illuminatedwith the guided surface wave will respond with an identifier. Theidentifier may be a unique identifier to distinguish the tag 402 fromall other tags 402, such as an IPv6 address or identifier in anotherformat. The guided surface wave of the first frequency has enough energydensity over the covered area, which may be up to the entire planet, toilluminate all tags 402 within the covered area. As a result, the tags402 may continually re-radiate by emitting its return signal, which istypically done at a second frequency higher than the first frequency.Continually re-radiating a return signal may include repeating thereturn signal with no delay or a slight delay (e.g., up to five secondsin one embodiment, up to two seconds in another embodiment, up to onesecond in another embodiment, or up to 0.5 seconds in anotherembodiment) between return signal emissions. In some situations, tags402 may be programmed to respond at certain times, with certainperiodicity, or in response to a command to respond. In othersituations, tags 402 may be commanded not to respond at least for aspecified period of time (e.g., during a read operation of plural tagsthat employs a de-interleaving approach to accurately identify largenumbers of tags).

In one embodiment, as long as a tag 402 is in the area illuminated bythe guided surface wave of the first frequency, the tag 402 will radiateits identifier “all the time” (e.g., repeatedly radiate the identifierover and over again with no or little delay between each radiationcycle) and for the life-cycle of the tag 402. As such, the tag 402 maybe tracked anywhere in the area illuminated by the guided surface waveof the first frequency as long as the tag 402 is within operative rangeof a receiver 408 that is configured to detect return signals on theemission frequency of the tag 402 (e.g., the second frequency). Aspreviously described, the location (e.g., longitude and latitude) andelevation of a tag 402 may be determined using, for example,triangulation or by using a receiver's location as a proxy for the tag'slocation.

In the exemplary embodiment where the covered area is the entire world,each compatible tag 402 may be tracked anywhere on the planet at anytime until the tag 402 stops transmitting. The tag 402 may stoptransmitting by being deactivated in response to a deactivation command,by failure of the tag circuitry 414, by becoming physically damaged,etc. In the global embodiment, the guided surface wave may be operativeto illuminate tags 402 at a relatively high altitude, such as up toabout 35,000 feet. As such, tags 402 carried by an aircraft may betracked provided a receiver can detect the reply signals from the tags402.

Receivers 408 may be positioned at any location where tag 402identification is desired. A non-exhaustive list of possible locationsfor receivers 408 includes manufacturing facilities, farms, warehouses,fulfillment centers that process Internet orders or mail orders forgoods, retail locations, restaurants, grocers, ports of entry for acountry, seaports, airports, along roadways, along railroad tracks, andon moving vehicles (e.g., cars, trucks, planes, ships, trains, forktrucks, etc.).

The widespread deployment of receivers 408 may allow for lifetimetracking of an object 404 that is associated with a tag 402. The amountof tracking information that is collected may depend on, for example,the nature of the object 404 associated with the tag 402, a supply chainof interest, or the interest level of persons or entities that have arelationship to the object. As an example, an object 404 may beassociated with a tag 402 at the time of manufacture or packaging in afactory in Beijing, China and then tracked when loaded on a truck anddriven to a seaport in Tianjin, China. Next, the object 404 is trackedwhen it is loaded on a cargo container and tracked when the cargocontainer is loaded onto a ship. The object 404 may be further trackedin route by the ship to a seaport in Los Angeles, Calif., U.S. Theunloading of the cargo container from the ship and the subsequentloading of the object 404 on a train may be tracked at the seaport byreceipt of the return signals from the tag 402. The object 404 may betracked during travel by train, which may take the object to Memphis,Tenn., U.S. where it is unloaded from the train and transported to ashelf in a fulfillment center in Memphis. An order for the object from acustomer in Boston, Mass., U.S. may be received by the operator of thefulfillment center. At that point, the object 404 may be removed fromthe shelf, placed in a shipping box, transported to a package deliverycarrier's Memphis sorting and distribution center where the boxcontaining the object is ultimately loaded on a plane. All of thoseevents also may be tracked. The object may be tracked as the planetravels to Boston. Then tracked are events such as the offloading of theobject from the plane, the transportation of the object to the packagedelivery carrier's Boston sorting and distribution center, the loadingof the object on a delivery truck and ultimate delivery to the customerworkplace or residence. Later, the customer may travel with the object404 on vacation to Paris, France. Assuming that the associated tag 402is not separated from the object or disabled, the object may be detectedagain during travel to, or while in, Paris.

It will be recognized that the foregoing object lifecycle trackingexample describes a representative supply chain situation. Objects thatare tracked using tags 402 that are responsive to guided surface wavesmay enter and pass through commerce in many other ways, but still may betracked for a variety of purposes. Those purposes include, for example,supply chain management, inventory management, detecting theft,estimating time of arrival at a location, etc.

Detailed information regarding where an object has been, and/or personsor entities that have interacted with the object, may be used in anumber of contexts. As an example, the identity of a purchaser of theobject may be determined together with the vendor of the object, theretail location (if applicable) and the manner of payment (e.g.,including a specific credit card, if applicable). This information maybe combined and analyzed with other information about the purchaser togenerate marketing opportunities, to automatically register the productfor warranty, for follow-up service/product update purposes, or forother reasons.

In one embodiment, the disclosed identification and tracking techniquemay be used to trace the origins of a breakout of a food-borne illness.In this embodiment, the stricken persons may be interviewed to determinewhat the people ate, when they ate those items, and the source of thefood to the person (e.g., the restaurant at which food was consumed orthe grocery at which food was purchased). The information for eachaffected person may be populated into a database and crossed referencedto determined which food item most likely caused the illness. Sometimesmerely cross referencing this information may not be sufficient todetermine the food that contains a pathogen, especially if the food isdistributed across wide areas of a country or region. Using informationcollected from the tags 402 associated with objects in the food supplychain may be of use in discovering which food is making people sick,where that food came from and where in the distribution chain otherpotentially contaminated food is currently located.

For this purpose, tags 402 may be associated with food items as early aspossible in the food chain. For instance, tags 402 may be associatedwith jars of peanut butter or boxes of multiple jars of peanut butter atthe processing plant that manufacturers the peanut butter and/or fillsthe jars. Produce (e.g., fruits and vegetables) may be associated withtags 402 at the grower or a packing facility that packages the produce(e.g., typically by placing the produce in containers or crates fordistribution and, in some embodiments, in which the produce is sold toconsumers). The location of the tags 402 may be tracked as describedabove. Then, during a food-borne illness outbreak, the stricken personinformation may be cross-referenced against the location trackinginformation in an attempt to identify a correspondence between thesickened people and a food product from a group or category of suspectedfood products, a food product that had an end distribution pattern nearthe locations of the sickened persons, or a food product classified insome other manner. In this manner, identification of the culprit foodproduct may be identified rapidly. It is contemplated that culpritproduct identification may be made faster than if conventional analysisis made.

Once the culprit food product is identified, the food product may berecalled. The tracking information may be used both downstream andupstream to facilitate product recall and other remedial actions. Forexample, the site at which the pathogen was introduced may be identifiedand the pathogen may be eradicated. Also, the last detected location offood units that might be contaminated and/or subject to recall may beidentified. If those items are still at grocers or restaurants, thegrocer or restaurant may be alerted and the food may be pulled from saleor use. Also, for product that was purchased by a consumer, the specificpurchaser of some of the items may be identified and contacted usingrecords establishing a correlation between purchaser and tagged object.In some embodiments, return signals may be analyzed to identify thepresent location of recalled units and action may be taken to retrievethose units from restaurants, homes, grocers or other locations.

Another example application is the tracking of items that are due forservice, or product upgrade or recall. An exemplary embodiment of aproduct recall with respect to a car will be described, butmodifications to the method for situations involving routine service ofproduct upgrade will be apparent without further explanation. In thisembodiment, the probe P emits a guided surface wave that illuminatestags P associated with cars. Receivers 408 are positioned alongroadways, parking areas, driveways or other locations that cars maypass. As a car passes one of the receivers 408, the return signal fromthe associated tag 402 will be received by the receiver 408. The tagidentifier or vehicle data associated with the tag identifier, such as avehicle identification number (VIN), may be cross-referenced against adatabase that stores which cars, by make and model, have completednecessary work to address a product safety recall. Data regardingcompletion of recall work may be obtained from car dealers and otherservice providers as the work is performed. If the vehicle is determinedto have completed the work, no additional action may be taken. If thevehicle is determined to have not completed the work, additional actionmay be taken. For instance, data may be transmitted to the tag 402 viaan encoded carrier message in the guided surface wave. The data mayprompt the tag 402 to interface with electronics of the vehicle todisplay a message to the driver that there is a product recall thatshould be addressed. Other actions may include attempting to contact anowner of the vehicle or an enforcement authority by phone, email, textor data message, convention mail, etc.

Another application may be charging a driver or vehicle owner for use ofa toll road. In this example, receivers 408 may be positioned at theentrances and exits from the toll road, or along the toll road. Asreturn signals from tags 402 associated with the vehicles or driversthat pass the receivers 408 are received, appropriate charges may bemade against an account or credit card that has been previouslyassociated with the driver or vehicle in the computer system 418.

In another embodiment, return signals from tags 402 or the lack of areturn signal may be used to identify counterfeit goods or authenticatelegitimate goods. In one exemplary approach, each legitimate object isassociated with a tag 402 having a unique identifier. At various times,the tag identifier may be checked against a database of tag identifiersthat are known to be associated with legitimate goods. Exemplary timesat which goods are checked may include at the time of passing through acustoms control checkpoint and when possession or title in the goods aretransferred between parties (e.g., from manufacturer to importer, fromimporter to distributor, from distributor to store owner, from storeowner to consumer). If there is a match between the received tagidentifier and the database of known legitimate tag identifiers, thegoods may be cleared by the customs authority or accepted by thereceiving party. If there is not a match or no tag 402 is present, thecustoms authority may confiscate the goods and perform an investigationor the receiving party may reject the goods.

As is evident from the foregoing example, the amount of tracking anddata collected with respect to various objects 404 will depend on thedegree of interest in the objects 404 and the reason for tracking theobject 404. Beyond tracking of an object 404, the associated tag 402 maybe used for additional purposes. Examples will be provided. In theseexamples, data may be transferred to the tag 402 or queries or commandsmay be transmitted to the tag 402. In these situations, the data, queryor command may be transmitted by way of a communication link between thetag 402 and a receiver 404 or may be encoded in a message addressed tothe tag 402 and forming part of the guided surface wave (e.g., as anencoded carrier message).

In one embodiment, data in addition to the tag identifier may be storedby the tag 402. The stored data, or selected elements of the storeddata, may be transmitted as part of an automated return signal. In othersituations, the stored data, or selected elements of the stored data,may be transmitted in a signal responsive to a query or command.Information stored by the tag 402 may change over time as is appropriateto support operational functionality. Stored data elements may include,but are not limited to, locations at which presence of the tag 402 waspreviously determined (e.g., a location history record); identifiers ofreceivers 408 that received a return signal from the tag 402; anidentity or location of the manufacturer, importer, distributor or ownerof the object 404 that is associated with the tag 402; time and date ofmanufacture, packaging or other processing; an association of one ormore additional objects 404 with the tag 402; customs clearance data;location, time and date, and/or other details related to certain eventssuch as crossing a port of entry, manufacture, purchase, purchaseamount, etc.; a product expiration date; a version number or value;product functions; a website or other data store from which more productinformation, warranty information, legal terms, or intellectual propertycoverage information is available; information about obtaining productsupport or ordering accessories or replacement parts; etc.

In various embodiments, the guided surface wave will be present overlong periods of time to illuminate tags 402 over large geographic areas.At some point, the value of a return signal for certain products may nolonger be of interest to one or more parties. For example, a purchaserof an object 404 may not wish to have the object's tag 402 send returnsignals due to privacy concerns. As another example, after food isconsumed, a tag 402 associated with the food's packaging is of littlevalue. In these situations, it may be possible to recycle tags, destroytags, turn the return signal feature of the tags off, contact a trackingdata system (e.g., the computer system 418) and opt out of furthertracking of tags, or other action that alters the operation of the tags,receivers or computer system.

In one embodiment, tags 402 may be responsive to guided surface waves ofmore than one frequency. For instance, a tag 402 may emit a first returnsignal when in the presence of a guided surface wave of a firstfrequency that is produced by a first probe and covers a widespread areaas described in connection with FIG. 25 and may emit a second returnsignal when in the presence of a guided surface wave of a secondfrequency that is produced by a second probe and covers a local area(e.g., an area corresponding to specific site) as described inconnection with FIG. 24. The return signal responsive to the wide-areaguided surface wave of the first frequency may be at a frequency that isdifferent than the frequency of the return signal of the local-areaguided surface wave of the second frequency. In this manner, the returnsignals may be distinguished and/or received by different receivers 408.

2(G). Computer System

The computer system in the various embodiments may be any appropriatesystem, such a personal computer, a server or a distributed system(e.g., a “cloud” computing environment). With additional reference toFIG. 26, an exemplary computer system 418 communicatively coupled with areceiver 408 is illustrated. If appropriate, the computer system 418 maycommunicate with plural receivers 408. If applicable, the computersystem 418 may have operable communication with one or more probes P tocontrol when the probes 300 generate a guided surface wave andcharacteristics of the guided surface waves, and to control the probes300 to include data or commands for transmission to one or more tags 402in the guided surface waves.

The computer system 418, together with the receivers 408, probes P andtags 402, may carry out the techniques that are described in thisdisclosure. As indicated, the computer system 418 communicates with thereceiver 408 over any appropriate communications medium 420. In additionto carrying out the operations described herein, the computer system 418may be a central registration system or some other form of managementplatform to manage the logical association of tags 402 with objects 404.

The computer system 418 may be implemented as a computer-based systemthat is capable of executing computer applications (e.g., softwareprograms), including a tag management function 448 that, when executed,carries out functions of the computer system 418 that are describedherein. The tag management function 448 and a database 450 may be storedon a non-transitory computer readable medium, such as a memory 452. Thedatabase 450 may be used to store various information sets used to carryout the functions described in this disclosure. The memory 452 may be amagnetic, optical or electronic storage device (e.g., hard disk, opticaldisk, flash memory, etc.), and may comprise several devices, includingvolatile and non-volatile memory components. Accordingly, the memory 452may include, for example, random access memory (RAM) for acting assystem memory, read-only memory (ROM), solid-state drives, hard disks,optical disks (e.g., CDs and DVDs), tapes, flash devices and/or othermemory components, plus associated drives, players and/or readers forthe memory devices.

To execute logical operations, the computer system 418 may include oneor more processors 454 used to execute instructions that carry out logicroutines. The processor 454 and the memory 452 may be coupled using alocal interface 456. The local interface 456 may be, for example, a databus with accompanying control bus, a network, or other subsystem.

The computer system 418 may have various input/output (I/O) interfacesfor operatively connecting to various peripheral devices. The computersystem 418 also may have one or more communications interfaces 458. Thecommunications interface 458 may include for example, a modem and/or anetwork interface card. The communications interface 458 may enable thecomputer system 418 to send and receive data signals to and from othercomputing devices, the receivers 408 and the probes P via thecommunications medium 420. In particular, the communications interface458 may operatively connect the computer system 418 to thecommunications medium 420.

The receiver 408 includes communications circuitry, such as radiocircuitry 460 to receive return signals from the tags 402 and acommunications interface 462 to establish operable communications withother devices over the communications medium 420. The radio circuitry460 may include one or more antennas and radio receivers (ortransceivers in the case where the receiver 408 transmits data orcommands to the tags 402).

Overall functionality of the receiver 408 may be controlled by a controlcircuit 464 that includes, for example a processing device for executinglogical instructions. The receiver 408 also may include a memory 466 forstoring data and the logical instructions in the form of executablecode. The memory 466 may be a non-transitory computer readable mediumsuch as one or more of a buffer, a flash memory, a hard drive, aremovable media, a volatile memory, a non-volatile memory, a randomaccess memory (RAM), or other suitable device. In a typical arrangement,the memory 466 includes a non-volatile memory for long term data storageand a volatile memory that functions as system memory for the controlcircuit 464. The receiver 408 may include any other appropriatecomponents such as, but not limited to, a display, a speaker, amicrophone, a user interface (e.g., a keypad and/or a touch-sensitiveinput), motion sensors, location determining elements (e.g., a GPSreceiver), etc.

3. CONCLUSION

Features that are described and/or illustrated with respect to oneembodiment may be used in the same way or in a similar way in one ormore other embodiments and/or in combination with or instead of thefeatures of the other embodiments. Therefore, any one disclosed featuremay be combinable or interchangeable with any other features.

Furthermore, although certain embodiments have been shown and described,it is understood that equivalents and modifications falling within thescope of the appended claims will occur to others who are skilled in theart upon the reading and understanding of this specification.

1. A method of tracking an object, comprising: producing a guidedsurface wave with a guided surface waveguide probe comprising a chargeterminal elevated over a terrestrial medium by generating at least oneresultant field that synthesizes a wave front incident at a complexBrewster angle of incidence (θ_(i,B)) of the terrestrial medium, theguided surface wave having sufficient energy density to power objectidentification tags across an area of interest; receiving return signalsfrom a tag of interest at plural receivers, the tag of interestassociated with an object and the receivers that receive the returnsignals change over time as the tag moves with the associated object inthe area of interest; and identifying a series of geolocations at whichthe object was present as a function of time according to the receivedreply signals from the tag.
 2. (canceled)
 3. The method of claim 1,wherein at least one of the geolocations in the series is determined bytriangulation using a corresponding return signal that is received attwo receivers.
 4. The method of claim 1, wherein at least one of thegeolocations in the series is a geolocation of the receiver thatreceives a return signal from the tag, the geolocation of the receiverserving as a proxy for the geolocation location of the object.
 5. Themethod of claim 1, further comprising storing the series of locations ina computer system and recalling the locations to determine a history oftravel for the object.
 6. The method of claim 1, wherein the object ofinterest is an instance of a food product originating from a supplierand the method further comprises tracking the locations of multipleinstances of the food product from the same supplier andcross-referencing end locations of the instances of the food productswith locations where persons are determined to have become ill with afood borne illness to determine if the food product made the personsill.
 7. The method of claim 6, further comprising identifying currentlocations of unused or unsold instances of the food product according toreturn signals received from tags associated with the instances of thefood product.
 8. The method of claim 6, further comprising tracing theinstances of the food products to a common point of origin.
 9. A systemfor tracking an object, comprising: a guided surface waveguide probecomprising a charge terminal elevated over a terrestrial medium thatproduces a guided surface wave by generating at least one resultantfield that synthesizes a wave front incident at a complex Brewster angleof incidence (θ_(i,B)) of the terrestrial medium, from which objectidentification tags obtain electrical power to operate across an area ofinterest, each tag associated with an object; a plurality of receiversdeployed at strategic locations to receive return signals from one ormore of the tags as the tags move with the associated objects during alifecycle of the objects; and a computer system operatively coupled withthe receivers, the computer system configured to identify a series ofgeolocations at which the object was present as a function of timeaccording to the received reply signals from the tag.
 10. (canceled) 11.The system of claim 9, wherein at least one of the geolocations in theseries is determined by triangulation using a corresponding returnsignal that is received at two receivers.
 12. The system of claim 9,wherein at least one of the geolocations in the series is a geolocationof the receiver that receives a return signal from the tag, thegeolocation of the receiver serving as a proxy for the geolocationlocation of the object.
 13. The system of claim 9, wherein the computersystem stores the series of locations and recalls the locations todetermine a history of travel for the object.
 14. The system of claim 9,wherein the object of interest is an instance of a food productoriginating from a supplier and the computer system tracks the locationsof multiple instances of the food product from the same supplier andcross-references end locations of the instances of the food productswith locations where persons are determined to have become ill with afood borne illness to determine if the food product made the personsill.
 15. The system of claim 14, wherein the computer system identifiescurrent locations of unused or unsold instances of the food productaccording to return signals received from tags associated with theinstances of the food product.
 16. The system of claim 14, wherein thecomputer system traces the instances of the food products to a commonpoint of origin.
 17. A method of tracking an object, comprising:producing a guided surface wave with a guided surface waveguide probe,the guided surface wave having sufficient energy density to power objectidentification tags across an area of interest; receiving return signalsfrom a tag of interest at plural receivers, the tag of interestassociated with an object and the receivers that receive the returnsignals change over time as the tag moves with the associated object inthe area of interest; and identifying a series of geolocations at whichthe object was present as a function of time according to the receivedreply signals from the tag, wherein at least one of the geolocations inthe series is determined by triangulation using a corresponding returnsignal that is received at two receivers.